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HYDRAULIC ENGINEERING 

AND 

MAN UAL 

FOR 


WATER SUPPLY ENGINEERS. 












































■ 












PUBLIC FOUNTAIN, CINCINNATI. 




















































A 


PRACTICAL TREATISE 

ON 


HYDRAULIC AND 

Water-Supply Engineering: 

RELATING TO THE 

HYDROLOGY, HYDRODYNAMICS, AND PRACTICAL 
CONSTRUCTION OF WATER-WORKS, IN 
NORTH AMERICA. 


WITH NUMEROUS 

TABLES AND ILLUSTRATIONS, 


/C / 

s by 

A" j.vr. PANNING, C.E., 

n 


MEMBER OF THE AMERICAN SOCIETV OF CIVIL ENGINEERS; FELLOW OF THE AMERICAN 
ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE ; MEMBER OF THE AMERICAN 
PUBLIC HEALTH ASSOCIATION ; MEMBER OF THE NEW ENGLAND 
AND THE AMERICAN WATER WORKS ASSOCIATIONS. 


FIFTH EDITION, REVISED, ENLARGED, 
AND NEW TABLES AND ILLUSTRATION^" ADDED. 

/ N 0 

NEW YORK: 

D. VAN NOSTRAND, PUBLISHER, 

23 MURRAY STREET & 27 WARREN STREET. 

188G. 


JUN 301886,/; 


V /■V<T/ P 

i/VASH' vVv 





Copyright, 1877, 


1886, 

BT 

J. T. FANNING. 



Electrotyped by 
SMITH & McDOUGAL. 


Printed by 
H. J. HEWITT. 





PREFACE. 


T I UIERE is at present no sanitary subject of more general 
interest, or attracting more general attention, than that 
relating to the abundance and wholesomeness of domestic water 
supplies. 

Each citizen of a densely populated municipality must of 
necessity be personally interested in either its physiological or 
its financial bearing, or in both. Each closely settled town and 
city must give the subject earnest consideration early in its ex¬ 
istence. 

At the close of the year 1875, fifty of the chief cities of the 
American Union had provided themselves with public water sup¬ 
plies at an aggregate cost of not less than ninety-five million 
dollars, and two hundred and fifty lesser cities and towns were 
also provided with liberal public Avater supplies at an aggregate 
cost of not less than fifty-five million dollars. 

The amount of capital annually invested in newly inaugurated 
water-works is already a large sum, and is increasing, yet the 
entire American literature relating to water-supply engineering 
exists, as yet, almost wholly in reports upon individual works, 
usually in pamphlet form, and accessible each to but compara¬ 
tively few of those especially interested in the subject. 

Scores of municipal water commissions receive appointment 
each year in the growing young cities of the Union, who have to 
inform themselves, and pass judgment upon, sources and systems 



VI 


PREFACE. 


of water supply, which are to become helpful or burdensome to 
the communities they are intended to encourage accordingly as 
the works prove successful or partially failures. 

The individual members of these “ Boards of Water Commis¬ 
sioners/’ resident in towns where water supplies upon an extended 
scale are not in operation, have rarely had opportunity to observe 
and become familiar with the varied practical details and appa¬ 
ratus of a water supply, or to acquaint themselves with even the 
elementary principles governing the design of the several different 
systems of supply, or reasons why one system is most advanta¬ 
geous under one set of local circumstances and another system 
is superior and preferable under other circumstances. 

A numerous band of engineering students are graduated each 
year and enter the field, many of whom choose the specialty of 
hydraulics, and soon discover that their chosen science is great 
among the most noble of the sciences, and that its mastery, in 
theory and practice, is a work of many years of studious acquire¬ 
ment and labor. They discover also that the accessible literature 
of their profession, in the English language, is intended for the 
class-room rather than the field, and that its formulae are based 
chiefly upon very limited philosophical experiments of a century 
and more ago but partially applicable to the extended range of 
modern practice. 

Among the objects of the author in the compilation of the 
following pioneer treatise upon American Water-works are, to 
supply water-commissioners with a general review of the best 
methods practised in supplying towns and cities with water, and 
with facts and suggestions that will enable them to compare in¬ 
telligently the merits and objectionable features of the different 
potable water sources within their reach ; to present to junior and 
assistant hydraulic engineers a condensed summary of those ele¬ 
mentary theoretical principles and the involved formulas adapted 
to modern practice, which they will have frequently to apply, 
together with some useful practical observations; to construct 
and gather, for the convenience of the older busy practitioners, 


PREFACE. 


vn 


numerous tables and statistics that will facilitate their calcula¬ 
tions, some of which would otherwise cost them, in the midst of 
pressing labors, as they did the author, a great deal of laborious 
research among rare and not easily procurable scientific treatises; 
and also to present to civil engineers generally a concise reference 
manual, relating to the hydrology, hydrodynamics, and practical 
construction of the water-supply branch of their profession. 

This work is intended more especially for those who have 
already had a task assigned them, and who, as commissioner, 
engineer, or assistant, are to proceed at once upon their recon- 
noissance and surveys, and the preparation of plans for a public 
water supply. To them it is humbly submitted, with the hope 
that it will prove in some degree useful. Its aim is to develop 
the bases and principles of construction, rather than to trace the 
origin of, or to describe individual works. It is, therefore, prac¬ 
tical in text, illustration, and arrangement; but it is hoped that 
the earnest, active young workers will find it in sympathy with 
their mood, and a practical introduction, as w T ell, to more pro¬ 
found and elegant treatises that unfold the highest delights of the 
science. 

Good design, w r hich is invariably founded upon sound mathe¬ 
matical and mechanical theory, is a first requisite for good and 
judicious practical engineering construction. We present, there¬ 
fore, the formulae, many of them new, which theory and practical 
experiments suggest as aids to preliminary studies for designs, 
and many tables based upon the formulas, which will facilitate the 
labors of the designer, and be useful as checks against his own com¬ 
putations, and we give in addition such discussions of the elemen¬ 
tary principles upon which the theories are founded as will enable 
the student to trace the origin of each formula; for a formula is 
often a treacherous guide unless each of its factors and experience 
coefficients are well understood. To this end, the theoretical dis¬ 
cussions are in familiar language, and the formulas in simple ar¬ 
rangement, so that a knowledge of elementary mathematics only 
is necessary to read and use them. 


PREFACE TO THE FIFTH EDITION. 


NEW chapter has been inserted in this Fifth 
Edition relating to Tank Stand-Pipes. Several 
new tables, new formulas, new illustrations, and new 
full-page plates have been inserted. 

In this revision, so much new matter has been 
added in various portions of the book that the entire 
work has been re-indexed. 


Minneapolis, Minn., 
March, 1886. 


J. T. F. 





































































. 
















































. 
































■ • ' 










































































IX 









































































































































CONTENTS. 


SECTION I. 

COLLECTION AND STORAGE OF WATER, AND ITS 

IMPURITIES. 


CHAPTER I. 

INTRODUCTORY.— Page 25. 

Art. 1, Necessity of Public Water Supplies.—2, Physiological Office of Water. 
—3, Sanitary Office of Water Supplies.—4, Helpful Influence of Public 
Water Supplies.—5, Municipal Control of Public Water Supplies.— 6 , 
Value as an Investment.—7, Incidental Advantages. 


CHAPTER II. 

QUANTITY OF WATER REQUIRED.— Page 31. 

Art. 8, Statistics of Water Supplied.—9, Census Statistics.—10, Approximate 
Consumption of Water.—n, Water Supplied to Ancient Cities.—12, Water 
Supplied to European Cities.—13, Water Supplied to American Cities.— 
14, The Use of Water Steadity Increasing.—15, Increase in Various Cities. 
—16, Relation of Supply per Capita to Total Population.—17, Monthly 
and Hourly Variations in the Draught.—18, Ratio of Monthly Consump¬ 
tion.—19, Illustrations of Varying Consumption.— 20, Reserve for Fire 
Extinguishment. 


CHAPTER II I. 

RAINFALL.— Page 45. 

Art. 21, The Vapory Elements of Water.—22, The Liquid and Gaseous Succes¬ 
sions.— 23, The Source of Showers.—24, General Rainfall.—25, Review of 
Rainfall Statistics.—26, Climatic Effects.—27, Sections of Maximum Rain¬ 
fall.— 28, Western Rain System.— 29, Central Rain System.— 30, Eastern 
Coast System.— 31, Influence of Elevation upon Precipitation.— 32, River 
Basin Rains.— 33, Grouped Rainfall Statistics.— 34, Monthly Fluctuations 







CONTENTS. 


in Rainfall.—35, Secular Fluctuations in Rainfall.—36, Local Physical 
and Meteorological Influences.—37, Uniform Effects of Natural Laws.— 
38, Great Rain Storms.—39, Maximum Ratios of Floods to Rainfalls.—40, 
Volume of Water from given Rainfalls.—41, Gauging Rainfalls. 


CHAPTER IV. 

FLOW OF STREAMS.— Page 65. 

Art. 42, Flood Volumes Inversely as the Areas of Basins.—43, Formulas for 
Flood Volumes.—44, Table of Flood Volumes.—45, Seasons of Floods.— 
46, Influence of Absorption and Evaporation upon Flow.—47, Flow in Sea¬ 
sons of Minimum Rainfall.—48, Periodic Classification of available Flow.— 
49, Sub-surface Equalizers of Flow.—50, Flashy and Steady Streams.— 
51, Peculiar Watersheds.—52, Summaries of Monthly Flow Statistics.— 
53, Minimum, Mean, and Flood Flow of Streams.—54, Ratios of Monthly 
Flow in Streams.—55, Mean Annual Flow of Streams.—56, Estimates of 
Flow of Streams.—57, Ordinary Flow of Streams.—58, Tables of Flow, 
Equivalent to given Depths of Rain. 

CHAPTER V. 

STORAGE AND EVAPORATION OF WATER.— Page 84. 

Storage. —Art. 59, Artificial Storage.— 60, Losses Incident to Storage.—61, 
Sub-strata of the Storage Basin.— 62, Percolation from Storage Basins.— 
63, Rights of Riparian Owners.—64, Periodical Classification of Riparian 
Rights.— 65, Compensations.— Evaporation. — 66, Loss from Reservoir 
by Evaporation.— 67, Evaporation Phenomena.— 68, Evaporation from 
Water.— 69, Evaporation from Earth.— 70, Examples of Evaporation.— 71, 
Ratios of Evaporation.— 72, Resultant Effect of Rain and Evaporation.— 
73, Practical Effect upon Storage. 

CHAPTER VI. 

SUPPLYING CAPACITY OF WATER-SHEDS.— Page 94. 

Art. 74, Estimate of Available Annual Flow of Streams.—75, Estimate of 
Monthly available Storage Required.—76, Additional Storage Required.— 
77, Utilization of Flood Flows.—78, Qualification of Deduced Ratios.—79, 
Influence of Storage upon a Continuous Supply.—80, Artificial Gathering 
Areas.—81, Recapitulation of Rainfall Ratios. 

CHAPTER VII. 

SPRINGS AND WELLS.— Page 102. 

Art. 82, Subterranean Waters.—83, Their Source, the Atmosphere.—84, Po¬ 
rosity of Earths and Rocks.—85, Percolations in the Upper Strata.—86, 
The Courses of Percolation.—87, Deep Percolations.—88, Subterranean 


CONTENTS. 


xi 


Reservoirs.—89, The Uncertainties of Subterranean Searches.—90, Re- 
novvned Application of Geological Science.—91, Conditions of Overflow¬ 
ing Wells.—92, Influence of Wells upon each other.—93, American Ar¬ 
tesian Wells.—94, Watersheds of Wells.—95, Evaporation from Soils.^ 
96, Supplying Capacity of Wells and Springs. 


CHAPTER VIII. 

IMPURITIES OF WATER.— Page 112. 

Art. 97, The Composition of Water.—98, Solutions in Water.—99, Properties 
of Water. 100, Physiological Effects of the Impurities of Water.—101, 
Mineral Impurities. 102, Organic Impurities.—103, Tables of Analyses 
of Potable W aters.—104, Ratios of Standard Gallons.—105, Atmospheric 
Impurities. 106, Sub-surface Impurities.—107, Deep-well Impurities.— 
108, Hardening Impurities.—109, Temperature of Deep Sub-surface 
Waters.—no, Decomposing Organic Impurities.—m, Vegetal Organic 
Impurities.—112, Vegetal Organisms in Water-pipes.—113, Animate Or¬ 
ganic Impurities.—114, Propagation of Aquatic Organisms.—115, Purify¬ 
ing Office of Aquatic Life.— 116, Intimate Relation between Grade of 
Organisms and Quality of Water.—117, Animate Organisms in Water- 
pipes.—118, Abrasion Impurities in Water.—119, Agricultural Impuru 
ties.— 120, Manufacturing Impurities.— 121, Sewage Impurities. — 122, 
Impure Ice in Drinking-Water.—123, A Scientific Definition of Polluted 
Water. 


CHAPTER IX. 

WELL, SPRING, LAKE, AND RIVER SUPPLIES.— Page 139. 

Well Waters. —Art. 124, Locations for Wells.—125, Fouling of Old Wells.— 
Spring Waters. —126, Harmless Impregnations.—127, Mineral Springs. 
—Lake Waters. —128, Favorite Supplies. —129, Chief Requisites.—130, 
Impounding.—131, Plant Growth.—132, Strata Conditions.—133, Plant 
and Insect Agencies.—134, Preservation of Purity.—135, Natural Clarifi¬ 
cation.—136, Great Lakes.—137, Dead Lakes.— River Waters. —138, 
Metropolitan Supplies.—139, Harmless and Beneficial Impregnations.— 
140, Pollutions.—141, Sanitary Discussions.—142, Inadmissible Polluting 
Liquids,—143, Precautionary Views.—144, Speculative Condition of the 
Pollution Question.—145, Spontaneous Purification.—146, Artificial Clari¬ 
fication.—147, A Sugar Test of the Quality of Water. 



Xll 


CONTENTS. 


SECTION II. 

FLOW OF WATER THROUGH SLUICES, PIPES, AND 

CHANNELS. 


CHAPTER X. 

WEIGHT, PRESSURE, AND MOTION OF WATER.— Page 161. 

Art. 148, Special Characteristics ofWater.—149, Atomic Theory.—150, Molec¬ 
ular Theory.—151, Influence of Caloric.—152, Relative Densities and 
Volumes.— Weight of Water. —153, Weight of Constituents of Water. 
—154, Crystalline Forms of Water.—155, Formula for Volumes at Differ¬ 
ent Temperatures.—156, Weight of Pond Water.—157, Compressibility 
and Elasticity ofWater.—158, Weights of Individual Molecules.—159, In¬ 
dividual Molecular Actions.— Pressure of Water. —160, Pressure Propor¬ 
tional to Depth.—161, Individual Molecular Reactions.— 162, Equilibrium 
destroyed by an Orifice.—163, Pressures from Vertical, Inclined, and Bent 
Columns of Water.—164, Artificial Pressure.—165, Pressure upon a Unit 
of Surface.—166, Equivalent Forces.— 167, Weight a Measure of Pressure. 
—168, A Line a Measure of Weight.—169, A Line a measure of Pressure 
upon a Surface.—170, Diagonal Force of Combined Pressures Graphically 
Represented.—171, Angular Resultant of a Force Graphically Repre¬ 
sented.—172, Angular Effects of a Force Represented by the Sine and 
Cosine of the Angle.— 173, Total Pressure.—174, Direction of Maximum 
Effect.— 175, Herizontal and Vertical Effects.— 176, Centres of Pressure 
and of Gravity.— 177, Pressure upon a Curved Surface, and Effect upon 
its Projected Plane.— 178, Centre of Pressure upon a Circular Area.— 
179, Combined Pressures.— 180, Sustaining Pressure upon Floating and 
Submerged Bodies.— 181, Upward Pressure upon a Submerged Lintel.— 
182, Atmospheric Pressure.— 183, Rise of Water into a Vacuum.— 184, 
Siphon.— 185, Transmission of Pressure to a Distance.— 186, Inverted 
Syphon. —187, Pressure Convertible into Motion.— Motion of Water. — 
188, Flow of Water.— 189, Action of Gravity upon Individual Molecules. 
— 190, Frictionless Movement of Molecules.— 191, Acceleration of Motion. 
— 192, Equations of Motion.— 193, Parabolic Path of Jet.— 194, Velocity of 
Efflux Proportional to the Head.— 195, Conversion of the Force of Grav¬ 
ity from Pressure into Motion.— 196, Resultant Effects of Pressure and 
Gravity upon the Motion of a Jet.— 197, Equal Pressures give Equal 
Velocities in all Directions.—198, Resistance of the Air.—199, Theoretical 
Velocities. 


CHAPTER XI. 

FLOW OF WATER THROUGH ORIFICES.— Page 194. 

Art. 200, Motion of the Individual Particles.—201, Theoretical Volume of 
Efflux.—202, Converging Path of Particles.—203, Classes of Orifices.— 



CONTEXTS. 


• • • 
xm 

204, Form of Submerged Orifice Jet.—205, Ratio of Minimum Section of 
Jet.—206, Volume of Efflux.—207, Coefficient of Efflux.—208, Maximum 
Velocity ol the Jet.—209, Factors ot the Coefficient of Efflux.—210, Prac¬ 
tical Use of a Coefficient.—211, Experimental Coefficients. (From Michel- 
otti, Abbe Bosset, Rennie, Castel, Lespinasse, General Ellis.)—212, Co¬ 
efficients Diagramed.—213, Effect of Varying the Head, or the Proportions 
of the Orifice.—214, Peculiarities of Efflux from an Orifice.—215, Mean 
Velocity of the Issuing Particles.—216, Coefficients of Velocity and 
Contraction.—217, Velocity of Particles Dependent upon their Angular 
Positions.—218, Equation of Volume of Efflux from a Submerged Orifice. 
—219, Effect of Outline of Geometrical Orifices upon Efflux.—220, Vari¬ 
able Value of Coefficients.—221, Assumed Mean Value of Efflux.—222, 
Circular Jets, Polygonal do., Complex do.—223, Cylindrical and Divergent 
Orifices.—224, Converging Orifices. 

CHAPTER XII. 

FLOW OF WATER THROUGH SHORT TUBES.— Page 213. 

Art. 225, An Ajutage.—226, Increase of Coefficient.—227, Adjutage Vacuum, 
and its Effect.— 228, Increased Volume of Efflux.— 229, Imperfect Va¬ 
cuum.—230, Divergent Tube.—231, Convergent Tube.—232, Additional 
Contraction.—233, Coefficients of Convergent Tubes.—234, Increase and 
Decrease of Coefficient of Smaller Diameter.—235, Coefficient of Final 
Velocity.— 236, Inward Projecting Ajutage.— 237, Compound Tube.— 
238, Coefficients of Compound Tubes.—239, Experiments with Cylindri¬ 
cal and Compound Tubes.—240, Tendency to Vacuum.—241, Percussive 
Force of Particles.—242, Range of Eytelwein’s Table.—243, Cylindrical 
Tubes to be Preferred. 


CHAPTER XIII. 

FLOW OF WATER THROUGH PIPES, UNDER PRESSURE.— 

Page 223. 

Art. 244, Pipe and Conduit.—245, Short Pipes give Greatest Discharge.—246, 
Theoretical Volume from Pipes.—247, Mean Efflux from Pipes.—248, Sub¬ 
division of the Head.—249, Mechanical Effect of the Efflux.—250, Ratio 
of Resistance at Entrance to the Pipe.— Resistance to Flow within 
A Pipe. —251, Resistance of Pipe-Wall.—252, Conversion of Velocity into 
Pressure.—253, Coefficients of Efflux from Pipes.—254, Reactions from the 
Pipe-Wall.—255, Origin of Formulas of Flow.—256, Formula of Resist¬ 
ance to Flow.—257, Coefficient of Flow.—258, Opposition of Gravity and 
Reaction.—259, Conversion of Pressure into Mechanical Effect.—260, 
Measure of Resistance to Flow—261, Resistance Inversely as the Square 
of the Velocity.—262, Increase of Bursting Pressure.—263, Acceleration 
and Resistance.—264, Equation of Head Required to Overcome the Re¬ 
sistance.—265, Designation of h" and /.—266, Variable Value of m .—267, 
Investigation of Values of m .—268, Definition of Symbols.—269, Experi- 


XIV 


CONTENTS. 


mental Values of the Coefficient of Flow.—270, Peculiarities of the Coeffi¬ 
cient (m) of Flow.—271, Effects of Tubercles.—272, Classification of Pipes 
and their Mean Coefficients.—273, Equation of the Velocity Neutralized 
by Resistance to Flow.—274, Equation of Resistance Head. —275, Equation 
of Total Head.—276, Equation of Volume.—277, Equation of Diameter.— 
278, Relative Value of Subdivisions of Total Head.—279, Many Popular 
Formulas Incomplete.—280.—Formula of M. Chezy.—281, Various Pop¬ 
ular Formulas Compared.—282, Sub-heads Compared.—283, Investiga¬ 
tions by Dubuat, and Coloumb, and Prony.—284, Prony’s Anal) r sis.—285, 
Eytelwein’s Equation of Resistance to Flow.—286, D’Abuisson’s Equation 
of Resistance to Flow.—287, Weisbach’s Equation of Resistance to Flow. 
—288, Transpositions of an Original Formula.—289, Unintelligent Use of 
Partial Formulas.—290, A Formula of more General Application.—291, 
Values of v for Given Slopes.—292, Values of h and h! for Given Velocities. 
—293, Classified Equations for Velocity, Head, Volume, and Diameter.— 
294, Coefficients of Entrance of Jet.—295, Mean Coefficients for Smooth* 
Rough, and Foul Pipes.—296, Mean Equations for Smooth, Rough, and 
Foul Pipes.—297, Modification of a Fundamental Equation of Velocity. 
—298, Values of c 1 . —299, Bends.—300, Branches.—301, How to Economize 
Head. 

CHAPTER XIV. 

MEASURING WEIRS, AND WEIR GAUGING.— Page 277. 

Art. 302, Gauged Volumes of Flow.—303, Form of Weir.—304, Dimensions. 
—305, Stability.—306, Varying Length.—307, End Contractions.—308, 
Crest Contractions.—309, Theory of Flow over a Weir.—310, Formulas 
for Flow, without and with Contractions.—311, Increase of Volume due 
to Initial Velocity of Water.—312, Coefficients for Weir Formulas.—313, 
Discharges for Given Depths.—314, Vacuum under the Crest.—315, Ex¬ 
amples of Initial Velocity.—316, Wide-crested Weirs.—317, Triangular- 
Notch Weirs.—318, Obstacles to Accurate Measures.—319, Hook Gauge. 
—320, Rule Gauge.—321, Tube and Scale Gauge. 

CHAPTER XV. 

FLOW OF WATER IN OPEN CHANNELS.— Page 299. 

Art. 322, Gravity the Origin of Flow.— 323, Resistance to Flow.— 324, Equa¬ 
tions of Resistance and Velocity.— 325, Equation of Inclination.— 326, Co¬ 
efficients of Flow for Channels.— 327, Observed Data of Flow in Channels. 
— 328, Table of Coefficients for Channels.— 329, Various Formulas of Flow 
Compared.— 330, Velocities of Given Films.— 331, Surface Velocities.— 
332, Ratios of Surface to Mean Velocities.— 333, Hydrometer Gaugings.— 
334, Tube Gauges— 335, Gauge Formulas.— 336, Pitot Tube Gauge— 337, 
Woltmann’s Tachometer.— 338, Hydrometer Coefficients.— 339, Henry’s 
Telegraphic Moulinet.— 340, Earlier Hydrometers.— 341, Double Floats.— 
342, Mid-depth Floats.— 343, Maximum Velocity Floats.— 344, Relative 
Velocities and Volumes due to Different Depths. 


CONTENTS. 


xv 


SECTION III. 

PRACTICAL CONSTRUCTION OF WATER-WORKS. 


CHAPTER XVI. 

RESERVOIR EMBANKMENTS AND CHAMBERS.— Page 333. 

Art. 345, Ultimate Economy of Skillful Construction.—346, Embankment Foun¬ 
dations.—347, Springs under Foundations.—348, Surface Soils.—349, Con¬ 
crete Cut-off Walls.—350, Treacherous Strata.—351, Embankment Core 
Materials.—352, Peculiar Pressures.—353, Earthwork Slopes.—354, Re¬ 
connaissance for Site.—355, Detailed Surveys.—356, Illustrative Case.— 
357, Cut-off Wall.—358, Embankment Core.—359, Frost Covering.—360, 
Slope Paving.—361, Puddle Wall.—362, Rubble Priming Wall.—363, A 
Light Embankment.—364, Distribution Reservoirs.—365, Application of 
Fine Sand.—366, Masonry—Faced Embankment.—367, Concrete Paving. 
368, Embankment Sluices and Pipes.—369, Gate Chambers.—370, Sluice 
Valve Areas.— 371, Stop-valve Indicator.— 372, Power required to Open 
a Valve,—373, Adjustable Effluent Pipe.— 374, Fish Screens.— 375, Gate 
Chamber Foundations.—376, Foundation Concrete.—377, Chamber 
Walls. 

CHAPTER XVII. 

OPEN CANALS. —Page 370. 

Art. 378, Canal Banks.—379, Inclinations and Velocities in Practice.—380, 
Ice Covering.—381, Table of Dimensions of Supply Canals.—382, Canal 
Gates.—383, Miners’ Canals. 

CHAPTER XVIII. 

WASTE WEIRS.— Page 377. 

Art. 384, The Office and Influence of a Waste-Weir.—385, Discharges over 
Waste-Weirs.—386, Required Lengths of Waste-Weirs.—387. Forms of 
Waste-Weirs.—388. Isolated Weirs.—389, Timber Weirs.—390, Ice-Thrust 
upon Storage Reservoir Weirs.—391, Breadths of Weir-Caps.—392, Thick¬ 
nesses of Waste-Weirs and Dams.—393, Force of Overflowing Water.— 
394, Heights of Waves. 

CHAPTER XIX. 

PARTITIONS AND RETAINING WALLS— Page 390. 

Art. 395, Design.—396, Theory of Water-Pressure upon a Vertical Surface.— 
397, Water Pressure upon an Inclined Surface.—398, Frictional Stability 



XVI 


CONTENTS. 


of Masonry.—399, Coefficients of Masonry Friction—400, Pressure Lever¬ 
age of Water.—401, Leverage Stability of Masonry.—402, Moment of 
Weight Leverage of Masonry—403, Thickness of a Vertical Rectangular 
Wall for Water Pressure.—404, Moments of Rectangular and Trapedoidal 
Sections.—405, Graphical Method of Finding the Leverage Resistance.— 
406, Granular Stability.—407, Limiting Pressures.—408, Table of Walls for 
Quiet Water.—409, Economic Profiles.—410, Theory of Earth Pressures. 
—411, Equation of Weight of Earth Wedge.—412, Equation of Pressure of 
Earth Wedge.—413, Equation of Moment of Pressure Leverage.—414, 
Thickness of a Vertical Rectangular Wall for Earth Pressure.—415, Sur¬ 
charged Earth Wedge.—416, Pressure of a Surcharged Earth Wedge.— 
417, Moment of a Surcharged Pressure Leverage.—418, Pressure of an 
Infinite Surcharge.—419, Resistance of Masonry Revetments.—420, Final 
Resultants in Revetments.—421. Table of Trapezoidal Revetments.—422, 
Curved-face Batter Equation.—423, Back Batters and their Equations.— 
424, Inclination of Foundation.— 425, Front Batters and Steps.—426, 
Top Breadth.—427, Wharf Walls.—428, Counterforted Walls.—429, Ele¬ 
ments of Failure.—430, End Supports.—431, Faced and Concrete Revet¬ 
ments. 


CHAPTER XX. 

MASONRY CONDUITS.— Page 431. 

Art. 432, Protection of Channels for Domestic Water Supplies.—433, Examples 
of Conduits.—434, Foundations of Conduits.—435, Conduit Shells.—436, 
Ventilation of Conduits.—437, Conduits under Pressure.—438, Protection 
from Frost.—439, Masonry to be Self-sustaining.—440, A Concrete Con¬ 
duit.—441, Example of a Conduit under Heavy Pressure.—442, Mean 
Radii of Conduits.—443, Formulas of Flow for Conduits.—444, Table of 
Conduit Data. 


CHAPTER XXI. 

MAINS AND DISTRIBUTION PIPES.— Page 446. 

Art. 445, Static Pressures in Pipes.—446, Thickness of Shell resisting Static 
Pressure.—447, Water-Ram.—448, Formulas of Thickness for Ductile 
Pipes.—449, Strengths of Wrought Pipe Metals.—450, Moulding of Pipes. 
—451, Casting of Pipes.—452, Formulas of Thickness for Cast-iron Pipes. 
453, Thicknesses found Graphically.—454, Table of Thicknesses of Cast- 
iron Pipes.—455, Table of Equivalent Fractional Expressions.—456, Cast- 
iron Pipe-Joints.—457, Dimensions of Pipe-Joints.—45S, Templets for 
Bolt Holes.—459, Flexible Pipe-Joint.—460, Thickness Formulas Com¬ 
pared.—461, Formulas for Weights of Cast-iron Pipes.—462, Table of 
Weights of Cast-iron Pipes.—463, Interchangeable Joints.—464, Charac¬ 
teristics of Pipe Metals.—465, Tests of Pipe-Metals.—466, The Preserva¬ 
tion of Pipe Surfaces.—467, Varnishes for Pipes and IronWork.—468, 
Hydraulic Proof of Pipes.—469, Special Pipes.—470, Cement-lined and 


CONTENTS. 


xvii 


Coated Pipes.—471, Methods of Lining.—472, Covering.—473, Cement 
Joints.—474, Cast Hub Joint.—475, Composite Branches.—476, Thickness 
of Shells for Cement Linings.—477, Gauge Thickness and Weights of 
Rolled Iron.—478, Lining. Covering, and Joint Mortar.—479, Asphaltum- 
Coated Wrought-iron Pipes.—480, Asphaltum Bath, for Pipes.—481, 
Wrought Pipe Plates.—482, Bored Pipes. — 483, Wyckoff’s Patent 
Pipe. 

CHAPTER XXI I. 

DISTRIBUTION SYSTEMS, AND APPENDAGES.— Page 493. 

Art. 484, Loss of Head by Friction.—485, Table of Frictional Heads in Pipes. 
—486, Relative Discharging Capacities of Pipes.—487, Table of Relative 
Capacities of Pipes.—488, Depths of Pipes.—489, Elementary Dimensions 
of Pipes.— 490, Distribution Systems.— 491, Rates of Consumption of 
Water.—492, Rates of Fire Supplies.—493, Diameter of Supply Main.— 
494, Diameters of Sub-mains.—495, Maximum Velocities of Flow.—496, 
Comparative Frictions.—497, Relative Rates of Flow for Domestic and 
Fire Supplies.—498, Required Diameters for Fire Supplies.—499, Duplica¬ 
tion Arrangement of Sub-Mains.—500, Stop-Valve Systems.—501, Stop- 
Valve Locations.—502, Blow-off and Waste Valves.—503, Stop-Valve De¬ 
tails.— 504, Valve Curbs.—505, Fire Hydrants.—506, Post Hydrants.—507, 
Hydrant Details.—508, Flush Hydrants.—509, Gate Hydrants.—510, High 
Pressures.—511, Air Valves.—512, Union of High and Low Services.—513, 
Combined Reservoir and Direct Systems.—514, Stand Pipes.—515, Fric¬ 
tional Heads in Service-Pipes. 


CHAPTER XXIII. 

CLARIFICATION OF WATER— Page 530. 

Art. 516, Rarity of Clear Waters.—517, Floating Debris.— 518, Mineral Sedi¬ 
ments.—519, Organic Sediments.—520, Organic Solutions.—521, Natural 
Processes of Clarification.—522, Chemical Processes of Clarification.—523, 
Charcoal Process.—524, Infiltration.—525, Infiltration Basins.—526, Ex¬ 
amples of Infiltration.—527, Practical Considerations.—528, Examples 
of European Infiltration.—529, Example of Intercepting Well.—530, 
Filter Beds.—531, Settling and Clear-Water Basins.—532, Introduction 
of Filter-Bed System.—533, Capacity of Filter Beds.-*-534, Cleaning of 
Filter Beds.—535, Renewal of Sand Surface.—536, Basin Coverings. 


CHAPTER XXIV. 


PUMPING OF WATER.— Page 557. 

Art. 537, Types of Pumps.—538, Prime Movers.—539, Expense of Variable 
Delivery of Water—540, Variable Motions of a Piston.—541, Ratios of 
Variable Delivery of Water.—542, Office of Stand-Pipe and Air-Vessel.— 


xviii 


CONTENTS. 


543, Capacities of Air-Vessels.—544, Valves.—545, Motions of Water 
through Pumps.—546, Double-Acting Pumping Engines.—547, Geared 
Pumping Engines.—548, Costs of Pumping Water.—549, Duty of 
Pumping Engines.—550, Special Trial Duties.—551, Economy of a High 
Duty. 


CHAPTER XXV. 

TANK STAND-PIPES. 

Art. 552, Their Function.—553, Foundations.—554, Wind Strains.—555, Ten¬ 
dency to Slide.—556, Tendency to Overturn.—557, Tank Materials.— 
558, Riveting.—559, Pressures in Inclosed Stand-Pipes.—560, Factors of 
Safety.—561, Grades of Metals.—562, Limiting Depths and Thicknesses 
of Metals.—563, Thicknesses of Metals Graphically Shown.—564, Exposed 
Stand-Pipes.—565, Stand-Pipe Data. 

CHAPTER XXVI. 

SYSTEMS OF WATER SUPPLY.— Page 603. 

Art. 566, Permanence of Supply Essential.—567, Methods of Gathering and 
Delivering Water. — 568, Choice of Water. — 569, Gravitation. — 570, 
Pumping with Reservoir Reserve.—571, Pumping with Direct Pressure. 


LIST OF TABLES 


Table No. Page 

1. Population, Families, and Dwellings in Fifty American Cities. 32 

1 a. Population, Families, and Dwellings in One Hundred American 

Cities in 1880. 33 a 

lb. Water Supplied to European Cities. 36 

2. Water Supplied, and Piping in several Cities. 38 

3. Water Supplied in years 1870 and 1874. 39 

4. Average Gallons of Water Supplied to each Inhabitant. 40 

5. Ratios of Monthly Consumption of Water in 1874. 43 

6. Mean Rainfall in different River Basins. 51 

7. Rainfall in the United States. 53 

8. Volumes of Rainfall per minute for given inches of Rain per twenty- 

four hours. 62 

9. Flood Volumes from given Watershed Areas. 67 

10. Summary of Rainfall upon the Cochituate Basin. 72 

11. Summary of Rainfall upon the Croton Basin. 72 

12. Summary of Rainfall upon the Croton West-Branch Basin. 73 

13. Summary of Percentage of Rain Flowing from the Cochituate Basin. 73 

14. Summary of Percentage of Rain Flowing from the Croton Basin. ... 73 

15. Summary of Percentage of Rain Flowing from the Croton West- 

Branch Basin. . 74 

16. Summary of Volume of Flow from the Cochituate Basin. 74 

17. Summary of Volume of Flow from the Croton Basin. 74 

18. Summary of Volume of Flow from the Croton West-Branch Basin.. 75 

19. Estimates of Minimum, Mean, and Maximum Flow of Streams.... 75 

20. Monthly Ratios of Flow of Streams. 76 

21. Ratios of Mean Monthly Rain and Inches of Rain Flowing each 

Month. 77 

22. Equivalent Volumes of Flow for given Depths of Rain in One 

Month. 82 

23. Equivalent Volumes of Flow for given Depths of Rain in One Year. 83 

23^. Statistics of Flow of Sudbury River, Mass. 83*3 

23 b. Summary of Rainfall on the Sudbury Basin. 83^ 

23c. Percentage of Rainfall Flowing from the Sudbury Basin. 83^ 

23d. Volume of Flow from the Sudbury Basin. 83^ 



























XX 


LIST OF TABLES. 


Table No. Page 

24. Evaporation from Water. 89 

25. Mean Evaporation from Earth. 89 

26. Monthly Ratios of Evaporation from Reservoirs. 92 

27. Multipliers for Equivalent Inches of Rain Evaporated. 92 

27a. Ratios and Equivalent Inches of Rain. 93 

27A Monthly Gains and Losses in Storage Reservoirs. 93 

28. Monthly Supply to and Draft from a Reservoir (with Compensation). 96 

29. Monthly Supply to and Draft from a Reservoir (without Compensa¬ 

tion. 97 

30. Ratios of Monthly Rain, Flow, Evaporation, and Consumption. 101 

30a. Estimate of Collectible Rainfall ... 101 

31. Percolation of Rain into One Square Mile of Porous Soil. ill 

32. Analyses of Various Lake, Spring, and Well Waters. 117 

33. Analyses of Various River and Brook Waters. .. 118 

34. Analyses of Various Streams in Massachusetts. 120 

35. Analyses of Various Water Supplies from Domestic Wells. 121 

36. Artesian Well Temperatures .. 127 

36 a. Analyses of Ice from a Stagnant Pond. 136 

37. Analyses of Various Mineral Spring Waters. 143 

38. Weights and Volumes of Water at Different Temperatures. 166 

39. Pressures of Water at Stated Depths. 172 

40. Correspondent Heights, Velocities, and Times of Falling Bodies... 190 

41. Coefficients from Michelotti’s Experiments with Orifices. 198 

42. Coefficients from Bossut’s Experiments with Orifices. 199 

43. Coefficients from Rennie’s Experiments with Orifices. 199 

44. Coefficients from Lespinasse’s Experiments with Orifices. 201 

45. Coefficients from General Ellis’s Experiments with Orifices. 203 

46. Coefficients for Rectangular Orifices (vertical). 205 

47. Coefficients for Rectangular Orifices (horizontal). 206 

48. Castel’s Experiments with Convergent Tubes. 217 

49. Venturi’s Experiments with Divergent Tubes. 219 

50. Eytelwein’s Experiments with Compound Tubes. 220 

51. Coefficients of Efflux ( c ) for Short Pipes. 227 

52 a. Experimental Coefficients of Flow, by H. Smith Jr. 236 

52. Experimental Coefficients of Flow ( m ) by Darcy. 237 

53. Experimental Coefficients of Flow (m) by Fanning. 238 

54. Experimental Coefficients of Flow ( m ) by Du Buat. 238 

55. Experimental Coefficients of Flow (///) by Bossut . 238 

56. Experimental Coefficients of Flow ( m ) by Couplet. 239 

57. Experimental Coefficients of Flow ( m ) by Provis. 239 

58. Experimental Coefficients of Flow (ni) by Rennie. 239 

59. Experimental Coefficients of Flow (m) by Darcy. 240 

60. Experimental Coefficients of Flow (m) by General Greene and others 240 

61. # Tabulated Series of Coefficients of Flow (m) . 242 

62. Coefficients for Clean, Slightly Tuberculated, and Foul Pipes. 248 

63. Various Formulas for Flow of Water in Pipes. 254 

64. Velocities (v) for given Slopes and Diameters. 259 













































LIST OF TABLES. xxi 

Table No. Page 

65. Tables of h and Ji due to given Velocities. 264 

66. Values of c v , and c for Tubes. 267 

66 a. Sub-coefficients of Flow (c 1 ) in Pipes. 271 

67. Coefficients of Resistance in Bends. 274 

68. Experimental Weir Coefficients. 288 

69. Coefficients for given Depths upon Weirs. 289 

70. Discharge for given Depths upon Weirs. 290 

71. Weir Coefficients by Castel....... 291 

72. Series of Weir Coefficients by Smeaton and others. 291 

73. Coefficients for Wide Weir-crests. 294 

73 a. Computed Weir Volumes. 298a 

74. Observed and Computed Flows in Canals and Rivers. 307 

75. Coefficients (;;/) for Open Channels. 308 

76. Various Formulas for Flow in Open Channels. 310 

77. Weights of Embankment Materials. 341 

78. Angles of Repose, and Frictions of Embankment Materials. 345 

79. Dimensions of Water Supply and Irrigation Canals. 373 

80. Waste-Weir Volumes for given Depths. 380 

81. Lengths and Discharges of Waste-Weirs and Dams. 381 

82. Thicknesses of Masonry Weirs and Dams. 387 

83. Heights of Reservoir and Lake Waves. 388 

84. Coefficients of Masonry Frictions. 396 

85. Computed Pressures in Masonry. 403 

86. Limiting Pressures upon Masonry.404 

87. Dimension of Walls to Retain Water. 406 

88. Dimension of Walls to Sustain Earth. 420 

89. Thicknesses of a Curved-face Wall.. 422 

90. Hydraulic Mean Radii for Circular Conduits. 442 

90 a. Coefficients ( m ) for Smooth Conduits. 444 

91. Conduit Data.445 

910. Coefficients of Flow in Conduits.445 

92. Tenacities of Wrought Pipe Metals. 451 

93. Thicknesses of Cast-iron Pipes. 455 

93 a. Thicknesses of Cast-iron Pipes as used in several Cities. 456 

94. Parts of an Inch and Foot expressed Decimally. 457 

95. Dimensions of Cast-iron Water-pipes. 461 

96. Flange Data of Flanged Cast-iron Pipes. 462 

97. Various Formulas for Thicknesses of Cast-iron Pipes. 466 

98. Weights of Cast-iron Pipes. 468 

98 a. Weights of Cast-iron Pipes as used in several Cities. 469 

99. Thicknesses of Wrought-iron Pipe Shells. 486 

100. Thicknesses and Weights of Iron Plates. 488 

101. Frictional Head in Pipes. 495 

102. Relative Discharging Capacities of Pipes. 500 

103. Depths to lay Water-pipes in different Latitudes. 502 

104. Elementary Dimensions of Pipes. 504 

105. Maximum Advisable Velocity of Flow in Pipes. 508 

















































XXII 


LIST OF TABLES. 


Table No. Page 

106. Diameters of Pipes to Supply given Numbers of Hose Streams.... 510 

107. Experimental Volumes of Fire Hydrant Streams. 520 

107 a. Pressure Lost by Friction in Hose. 520# 

107A Hydrant and Hose Stream Data. 520^ 

108. Frictional Head in Service Pipes. 528 

109. Dimensions of Filter-beds for given Volumes. 554 

no. Piston Spaces for given Arcs of Crank Motion. 562 

in. Ratios of Piston Motions for given Crank Arcs. 564 

112. Costs of Pumping in Various Cities. 575 

113. Special Trial Duties of Various Pumping Engines. 580 

114. Comparative Consumptions of Coal at Different Duties. 581 

115. Fuel Expenses for Pumping compared on Duty Bases. 582 

116. Comparison of Values of Pumping Engines on Fuel Bases. 584 

117. Tank Stabilities of Position. 589 

118. Pitch and Sizes of Rivets. 592 

119. Factors for Metal Tank Stand Pipes. 594 

120. Thickness of Sheets for Metal Stand Pipes. 596 

121. Experiments with Hollow Cylindrical Beams. 599 


f 



















LIST OF FULL PAGE ILLUSTRATIONS. 

*\ 


Page 

Public Fountain, Cincinnati. ii 

Tank Stand-Pipe, Fremont, O. ix 

Gateway, Chestnut Hill Reservoir, Boston. 24 

Pumping Station, Toledo. 31 

Diagram of Pumping, Annual. 42 

Pumping Station, Milwaukee. 45 

Diagrams of Rainfall. 55 

Diagrams of Rainfall. 57 

Diagrams of Secular Rainfall. 59 

Section and Plan of Pump-House. 65 

Sections of Croton New Aqueduct. 74 

Reservoir Embankment, Norwich. 84 

Croton Dam. 94 

Intercepting Well, Prospect Park, Brooklyn. 102 

Pumping Station, New Bedford. 139 

Stand-Pipe, Boston. 160 

Pumping Station, Manchester. 213 

Compound Duplex Pumping Engine. 223 

Measuring Weir, for Turbine Test. 277 

Modern Current Meters. 299 

Improved Current Meters... 325^ 

Fairmount Turbines and Pumps, Philadelphia. 331 

Distributing Reservoir. 333 

Sluice Valve. 364 

Compound Inverted Pumping Engine. 377 

Dam on Natchaug River. 391 

Conduit Sections. 431 

Cylindrical Penstock. 440 

Sections of Croton New Aqueduct. 445 

Forms of Pipe-Sockets and Spigots. 446 

Branch, Reducer and Bend. 478 

Double-Faced Stop-Valves. 493 

Plan of a Pipe System. 505 

Flush Fire Hydrants. 521 

Pumping-Engine, No. 3, Brooklyn. 557 

Cornish Plunge-Pump. 563 

Compound Beam Pumping-Engine, Lynn. 567 

Geared Pumping-Engine, Providence. 573 

Plan of Geared Pumping-Engine. 574 

Elevation of Geared Pumping-Engine. 575 

Front Elevation of Boiler. 580 

Side Elevation of Boiler. 581 

Tank Stand-Pipe, South Abington. 585 

Jonval Turbine. 593 

Hydraulic Power Pumping Machinery, Manchester. 603 

Whole Number of Illustrations . 200 


















































APPENDIX. 


Page 

Metric Weights and Measures... 6n 

Table of French Measures and United States Equivalents . 612 

Cubic Inch, and Equivalents. 613 

Gallon, and Equivalents. 613 

Cubic Foot, and Equivalents. 613 

Imperial Gallon, and Equivalents. 614 

Cubic Yard, and Equivalents. 614 

Table of Units of Heads and Pressures of Water, and Equivalents. 614 

Table of Average Weights, Strengths, and Elasticities of Materials. 616 

Formulas for Diameters and Strengths of Shafts. 617 

Trigonometrical Expressions. 617 

Trigonometrical Equivalents. 618 

Table of Sines, Tangents, &c. 619 

What Constitutes a Car Load. . 620 

Lubricating Compounds for Gears. 620 

Compound for Cleaning Brass. 620 

Iron Cement, for Repairing Cracks in Castings. 620 

Alloys, Table of. 621 

Velocities of Flow in Channels, that Move Sediments. 622 

Tensile Strengths of Cements and Mortars. 623 

Dimensions of Bolts and Nuts. 624 

General Water Works Statistics, 1880. 625 

Comparative Water Works Statistics. 626 

General Water Works Statistics, 1882. 627 

Stand-Pipe Data. 628 

Weights of Lead and Tin-lined Service-Pipes. 629 

Safe Weights of Lead Service-Pipes. 630 

Weights of Lead Pipes for given Pressures. 631 

Resuscitation from Apparent Death by Drowning. 632 







































GATEWAVT, CHESTNUT HILL RESERVOIR, BOSTON. 






















































































































































































































































































































































































































































































































































































































































































































































































































































SECTION I. 


Collection and Storage of Water, and its Impurities. 


CHAPTER I. 

INTRODUCTORY. 

1. Necessity of Public Water Supplies. —A new or 

an additional water supply is an inevitable necessity when¬ 
ever and wherever a new settlement establishes itself in an 
isolated position; again whenever the settlement receives 
any considerable increase; and again when it becomes a 
great metropolis or manufacturing centre. 

In all the wonderful and complex transformations in 
Nature, in the sustenance of all organized beings, and in 
the convenience and delight of man, water is appointed to 
perform an important and essential part. 

Life cannot long exist in either plant or animal, unless 
water, in some of its forms, is provided in due quantity. 

Wholesome water is indispensable in the preparation of 
all our foods ; clear and soft water is essential for promot¬ 
ing the cleanliness and health of our bodies; and pure 
water is demanded for a great variety of the operations of 
the useful and mechanic arts. 

2. Physiological Office of Water. — Of the three 
essentials to human life, air, water , and food, the one now 



26 


INTRODUCTORY. 


to be specially considered, water, lias for its physiological 
office to maintain all the tissues of the body in healthy 
action. 

If the water received into the system is unfit for such 
special duty, all the animal functions suffer and are weak¬ 
ened, air then but partially clarifies the blood, food then is 
imperfectly assimilated, and the body degenerates. 

Vigor is essential to the uniform success and happiness 
of every individual, and strength and happiness of the 
people are essential to good public morals, good public 
government, and sound public prosperity. 

Sanitary improvements are, therefore, among the first 
and chief duties of public officers and guardians, and have 
ever been the objects of the most earnest thought and labor 
of great public philanthropists. 

3. Sanitary Office of Public Water Supplies.— 
Water has thus far proved the most effectual and econom¬ 
ical agent, as sanitary scavenger, in the removal from our 
habitations of waste slops and sewage, and also the most 
effectual*"' and economical agency in the protection of life 
and property from destruction by fire. 

The necessity of a judiciously executed system of public 
water-supply increases as the population of a town increases; 
as the mass of buildings thickens; as the lands upon which 
the town is built become saturated with sewage, and the 
individual sources within the town are polluted; as the 
atmosphere over and within the town is fouled by gases 

* We need refer to but one of many experiences, viz.: At Columbus, 
Oliio, the average loss by fire for the four years preceding tlie completion of 
the public water-works was T 6 y 5 y of one per cent, of tlie valuation. The average 
loss during the first four years after the completion of the works was y^/y, and 
during the fifth year, from April 1 , 1875 , to April 1 , 187 G, was y^ of the valu¬ 
ation. These statistics show a probable saving in the first four years of upward 
of one-half million dollars, and in five years of more than the entire cost of the 
water-works. 



HELPFUL INFLUENCE OF PUBLIC WATER SUPPLIES. 27 

arising therefrom ; and as the dangers of epidemics, fevers, 
and contagious diseases increase. 

4. Helpful Influence of Public Water Supplies.— 

No town or city can submit to a continued want of an 
adequate supply of pure and wholesome water without a 
serious check in its prosperity. 

Capital is always wary of investment where the elements 
of safety and health are lacking, and industry dreads fre¬ 
quent failures and objectionable quality in its water supply. 

It is true that considerations of profit sometimes induce 
the assembling of a town where potable waters are procur¬ 
able with difficulty, but in such cases the lack is sure to 
prove a growing hindrance to its prosperity, and before the 
town arrives at considerable magnitude, its remedy will 
present one of the most difficult problems with which its 
municipal authorities are obliged to cope. 

In the experience of all large and thriving cities, there 
has come a time when an additional or new and abundant 
water supply was a necessity, terribly real, that would not 
be talked down, or resolved out of existence by public 
meetings, or wait for a more convenient season; a time 
when it was not possible for every citizen to supply his 
household or his place of business independently, or even 
for a majority of the citizens to do so, and when prompt, 
united, and systematic action must be taken to ensure the 
health, prosperity, and safety of the people. Such stern 
necessity often appears to present difficulties almost insur¬ 
mountable by the available mechanical and financial re¬ 
sources of the citizens. 

Out of such simple but positive necessities have grown 
the grandest illustrations, in our great public water sup¬ 
plies, of the benefits of co-operative action, recorded in the 
annals of political economy. Out of such simple necessi- 


28 


INTRODUCTORY. 


ties grew some of the most magnificent and enduring con¬ 
structions of the powerful empires of the Middle Ages, the 
architectural grandeur of which the moderns have not 
attempted to surpass. 

5. Municipal Control of Public Water Supplies. 

—The magnitude of the labors to be performed and tiie 
amount of capital required to be invested in the construc¬ 
tion of a system of water supplies invariably brings into 
prominence the question, Shall the construction, operation, 
and control of these works be entrusted to private capital, 
or shall they be executed under the patronage of the muni¬ 
cipal authorities and under the direction of a commission 
delegated by the people? The conclusion reached in a 
majority of the American cities has been that the works 
ought to be conducted as public enterprises. They have 
been believed to be so intimately connected with the public 
interests and welfare as to be peculiarly subjects for pub¬ 
lic promotion; and that, under the direction of a commis¬ 
sion appointed by the people to study and comprehend all 
their needs, to consider, with the aid of expert advice, and 
to suggest plans, the works would be projected on such a 
liberal and comprehensive scale as would best fulfil the 
objects desired to be attained, and that the true interests of 
the people would not be subordinated to mere considera¬ 
tions of profit. 

Further, that if the works when complete were operated 
under municipal care, their standard and effectiveness would 
more certainly be maintained; their extension into new 
territory might keep pace with and encourage the growth 
of the city ; they might not, by excessive rates, be made to 
oppress important industries ; their advantages might more 
surely be kept within the reach of the poorer classes ; they 
might more economically be applied to the adornment of 


INCIDENTAL ADVANTAGES. 


29 


the public buildings and grounds ; and that they might, 
when judiciously planned, constructed, and managed, be¬ 
come a source of public revenue. 

Nearly all the objects desirable to be attained in a pub¬ 
lic water supply have, however, been accomplished, in 
numerous instances that might be cited, under the auspices 
of private enterprise. 

G. Value as an Investment.— The necessary capital 
honestly applied to the construction of an intelligently and 
judiciously planned effective public water supply has 
almost invariably proved, both directly and indirectly, a 
remunerative investment. 

Many, though not all, of our American Water-supply 
Reports, show annual incomes from water-rates in excess 
of the combined annual operating expenses and interest on 
the capital expended. In addition to this cash return, there 
are in all cases benefits accruing to the public, usually 
exceeding in real value that of the more generally recog¬ 
nized money income. 

7. Incidental Advantages. —The construction of water¬ 
works is almost sure to enhance the value of property along 
its lines, under its protection, and availing of its conve¬ 
niences. There is, also, a perpetual reduction * in the 


* In a recently adopted schedule of the National Board of Underwriters, 
there are additions to a minimum standard rate in a standard city, which is 
provided with good water supply, fire alarm, police, etc., as follows, termed 
deficiency charges : 

Minimum standard rate of insurance of a standard building. . 25 cents. 


If no water supply.add 15 “ 

If only cisterns, or equivalent. “ 10 “ 

If system is other than gravity. “ 05 “ 

If no fire department. “ 25 “ 

If no police organization. “ 05 “ 

If no building law in force. “ 05 “ 


The financial value of the enhanced fire risk, as deduced by the Board from 
an immense mass of statistics, and the additional premium charged on the 









30 


INTRODUCTORY. 


yearly rates of insurance. Tlie substitution of soft water 
for hard water, as almost all waters are, results in a mate- 
rial reduction in the daily waste accompanying the jorepa- 
ration of foods, in laundry and cleansing operations, in the 
production of steam power, and in many of the processes 
employed in the useful arts. 

There are many industries, the introduction of which are 
of value to a community, that cannot be prosecuted with¬ 
out the use of tolerably pure and soft water. To save the 
annual aggregate of labor required to convey water from 
wells into and to the upper floors of city tenements or resi¬ 
dences, is a matter of no inconsiderable importance; but 
paramount to all these is the value of the sanitary results 
growing out of the maintenance of health, and the induce¬ 
ment to cleanliness of person and habitation, by the con¬ 
venience of an abundance of water delivered constantly in 
the household, and the enhanced safety to human life and 
to property from destroying flames, accompanying a liberal 
distribution of public fire hydrants under adequate pressure 
throughout the populous districts. 


most favorable buildings, is 60 per cent, without good water-works, and 40 pel 
cent, if only fire cisterns are provided. 


































































PUMPING STATION, TOLEDO. 










































































































































































































































































































































































































































































































































CHAPTER II. 


QUANTITY OF WATER REQUIRED. 

8. Statistics of Water Supplied. —One of tlie first 
duties of a Commission to whom lias been assigned the 
task of examining into and reporting upon a proposed 
supply of water for a community, is to determine not only 
wliat is a wholesome water, but what quantity of such 
wdiolesome water will be required, and adequate for its 
present and prospective uses. 

In many cases, this problem is parallel with the deter¬ 
mination of a product from two factors, one of which only 
is a known quantity. Often all factors must be assumed. 

The total number of inhabitants, the total number of 
dwellings, and the total number of manufacturing and 
commercial firms can be obtained without great difficulty, 
and it can safely be assumed that eighty per cent, of all 
these within reach of a new and improved water supply 
will be among its patrons within a few years after the intro¬ 
duction of the new supply; but how much water will be 
required for actual use, or will be wasted, per person, per 
dwelling, or per firm, is always quite uncertain. 

Rarely can any data worthy of confidence respecting 
these quantities be obtained. The practice, therefore, gen¬ 
erally is, to obtain statistics from towns and cities already 
supplied, and to attempt to reduce these to some general 
average that will apply to the case in hand. 

9. Census Statistics.—In a small portion of the water- 
supply reports there is given, in addition to the total quan- 


QUANTITY OF WATER REQUIRED. 


tity of water supplied, the number of families supplied ; in 
other reports, the number of dwellings, or the number of 
fixtures of the several classes supplied, and occasionally 
the population supplied, or the total population of the 
municipality. 

In the investigations for facts applicable to a new sup¬ 
ply, when information must necessarily be culled from 
various water reports, it is often desirable to know the 
populations of the places from which the reports are re¬ 
ceived, their number of families, persons to a family, num¬ 
ber of dwellings and persons to a dwelling, so as to be able 
to reduce their water-supply data to a uniform classifica¬ 
tion. We therefore present an abstract from the United 
States Census for the year 1870, giving such information 
respecting fifty prominent American cities, and similar data 
in table No. la, for the year 1880. 


TABLE No, 1 . 

Population, Families, and Dwellings in Fifty American Cities. 

IN THE YEAR 1870. 


CITIES. 

Size.* 

Population. 

Families. 

Dwellings. 

Number. 

Persons 
to a 
family. 

Numbar. 

Persons 
to a 

dwelling 

Albany, N. Y. 

20 

69,422 

14,105 

4.92 

8,748 

7-94 

Allegheny, Penn. 

2 3 

53 > i8 ° 

10,147 

5- 2 4 

8,347 

6-37 

Baltimore, Md. 

6 

267,354 

49,929 

5-35 

40 , 35 ° 

6.63 

Boston, Mass. 

7 

250,526 

48,188 

5.20 

29,623 

8.46 

Brooklyn, N. Y. 

3 

396,099 

80,066 

4-95 

45,834 

8.64 

Buffalo, N. Y. 

11 

117,74 

22,325 

5- 2 7 

18,285 

6.44 

Cambridge, Mass. 

33 

39,634 

7. 8 97 

5.02 

6,348 

6.24 

Charleston, S. C. 

26 

48,956 

9,098 

5-38 

6,861 

7 -i 4 

Charlestown, Mass... . 

47 

28,323 

6,155 

4.60 

4,396 

6 44 

Chicago, Ill. 

5 

298,977 

59,497 

5*°3 

44,620 

6.70 

Cincinnati, Ohio. 

8 

216,239 

42,937 

5*°4 

24,550 

8.81 


* This column expresses the order of size as numbered from largest to 
smallest; New York, the largest, being numbered 1 . 





































STATISTICS OF FIFTY AMERICAN CITIES. 


33 


I 


Population, Etc., in Fifty American Cities—( Continued ). 


CITIES. 

Size. 

Population. 

Families. 

Dwell 


Number, j 

Persons 
to a 
family. 

Number. 

Persons 
to a 

dwelling 

Cleveland, Ohio. 

I S 

92,829 

18,411 

5-°4 

16,692 

5 - 5 6 

Columbus, Ohio. 

42 

3 i > 2 74 

5 ^ 79 ° 

5 - 4 ° 

5 , 011 

6.24 

Dayton, Ohio. 

44 

30,473 

6,109 

4*99 

5 , 6 h 

5-43 

Detroit, Michigan. 

18 

79*577 

U . 6 36 

5-°9 

14,688 

5-42 

Fall River, Mass. 

5 ° 

26,766 

5 . 216 

5- J 3 

2,687 

9.96 

Hartford, Conn. 

34 

37 > i8 ° 

7.427 

5 - 0 ! 

6,688 

5 56 

Indianapolis, Ind. 

2 7 

48,244 

9,200 

5-24 

7,820 

6.17 

Jersey City, N. J. 

1 7 

82,546 

16,687 

4.95 

9,867 

8-37 

Kansas Citv, Mo. 

38 

32,260 

5.585 

5-78 

5,424 

5 95 

Lawrence, Mass. 

45 

28,921 

5. 2 87 

5.47 

3,443 

8.40 

Louisville, Ky. 

14 

IQ o ,753 

I 9. 1 7 7 

5.25 

14,670 

6.87 

Lowell, Mass. 

3 1 

40,928 

7.649 

5.35 

6,362 

6.43 

Lynn, Mass. 

49 

28,233 

6,100 

4.63 

4,625 

6.10 

Memphis, Tenn. 

3 2 

40,226 

7.824 

5- I 4 

6,408 

6.28 

Milwaukee, Wis. 

T 9 

7 I >44° 

14,226 

5-02 

13,048 

5-48 

Mobile, Ala. 

39 

32,034 

6,3°! 

5.08 

5,738 

5-58 

Newark, N. J. 

13 

io 5,°59 

21,631 

4.86 

i4,35o 

7-3 2 

New Haven, Conn.. .. 

2 5 

50,840 

10,482 

4.85 

8,100 

6.28 

New Orleans, La. 

9 

191,418 

39. U9 

4.89 

33,656 

5-69 

New York, N. Y. 

1 

942,292 

i8 5,7 8 9 

5-°7 

64,044 

14.72 

Paterson, N. J. 

37 

33,579 

7,048 

4.76 

4,653 

7.22 

Philadelphia, Pa. 

2 

674,022 

127.746 

5.28 

112,366 

6.01 

Pittsburg, Pa. ... 

16 

86,076 

16,182 

5.32 

14,224 

6.05 

Portland, Me. 

41 

3 I ,4 I 3 

6,632 

4.74 

4,836 

6.50 

Providence, R. I. 

21 

68,904 

1 4,7 7 5 

4.66 

9,227 

7.46 

Reading, Pa. 

3 6 

3303° 

6,93 2 

4.89 

6,294 

5-39 

Richmond, Va. 

24 

51038 

9.79 2 

5-21 

8,033 

6-35 

Rochester, N. Y. 

22 

62,386 

12,213 

5.11 

11,649 

5-36 

San Francisco, Cal.. .. 

10 

1 49’47 3 

3°,553 

4.89 

25,905 

5-77 

Savannah, Ga. 

48 

28,235 

5. OI 3 

5-63 

4,56i 

6.19 

Scranton, Pa. 

35 

3509 2 

6,642 

5.28 

5,646 

6.21 

St. Louis, Mo. 

4 

310,864 

59.431 

5.23 

39,675 

7.84 

Syracuse, N. Y. 

2 9 

4305 1 

8,677 

4.96 

7,088 

6.07 

Toledo, Ohio. 

40 

3F5 8 4 

6,457 

4.89 

6,069 

5.20 

Troy, N. Y. 

28 

46,465 

9.3° 2 

5.00 

5.893 

7.88 

Utica, N. Y. 

46 

28,804 

5.793 

4-97 

4,799 

6.00 

Washington, D. C. 

12 

109,199 

2 L343 

5- 12 

I 9.545 

5-59 

Wilmington, Del. 

43 

30,841 

5,808 

5-3 1 

5,398 

5-71 

Worcester, Mass. 

3° 

4Li°5 

8,658 

4-74 

4,922 

8*35 


3 






































































STATISTICS OF HUNDRED AMERICAN CITIES 


33a 


TABLE No. la. 

Population, Families, and Dwellings in ioo American Cities 

in the year 18S0. (.From the U. S. Censiis 0/1880.) 


CITIES. 

Size. 

Population 

Albany, N. Y. 

21 

90,758 

Allegheny, Pa. 

23 

78,682 

Atlanta, Ga. 

49 

37,409 

Auburn, N. Y. 

84 

21,924 

Augusta, Ga. 

86 

21,891 

Baltimore, Md. 

7 

332,313 

Bay City, Mich. 

95 

20,693 

Boston, Mass. 

5 

362,839 

Bridgeport, Conn... 

7 i 

27,643 

Brooklyn, N. Y. 

3 

566,663 

Buffalo, N. Y. 

13 

I 55 J 34 

Cambridge, Mass... 

3 i 

52,669 

Camden, N. ] . 

44 

41,659 

Charleston, S. C. 

36 

49,984 

Chelsea, Mass. 

88 

21,782 

Chicago, Ill... 

4 

503,185 

Cincinnati, Ohio. .. . 

8 

255439 

Cleveland, Ohio. 

11 

160,146 

Columbus, Ohio .... 

33 

51,647 

Covington. Ky. 

65 

29,720 

Davenport, Iowa. .. . 

87 

21,831 

Dayton, Ohio. 

47 

38,678 

Denver, Col. 

50 

35,629 

Des Moines, Iowa.. . 

80 

22,408 

Detroit, Mich. . 

18 

116,340 

Dubuque, Iowa. 

81 

22,254 

Elizabeth, N. J. 

69 

28,229 

Elmira, N. Y. 

97 

20,541 

Erie, Pa. 

70 

27,737 

Evansville, Ind. 

66 

29,280 

Fall River, Mass.... 

37 

48,961 

Fort Wayne, Ind.... 

74 

26,880 

Galveston, Texas.... 

82 

22,248 

Grand Rapids, Mich. 

58 

32,016 

Harrisburg, Pa. 

60 

30,762 

Hartford, Conn. 

43 

42,015 

Hoboken. N. f. 

59 

30,999 

Holyoke, Mass. 

85 

21,915 

Indianapolis, Inch... 

24 

75,056 

Jersey City, N. J. .. . 

17 

120,722 

Kansas City, Mo.... 

30 

55,785 

Lancaster, Pa. 

77 

25,769 

Lawrence, Mass. 

46 

39 , 1 5 T 

Louisville, Ky. 

16 

123,758 

Lowell, Mass. 

27 

59,475 

Lynn, Mass. 

48 

38,274 

Manchester, N. H. .. 

56 

32,630 

Memphis, Tenn. 

54 

33,592 


Families. 

Dwellings. 

Number. 

Persons to 
a family. 

Number. 

Persons 
to a 

dwelling. 

18,297 

4.96 

13,259 

6.85 

14,747 

5-34 

11,943 

6-59 

7,799 

4.80 

6,494 

5-76 

4 , 4 D 

4.96 

3,879 

5-65 

4,998 

4-38 

3,938 

5-56 

65,356 

5 -08 

50,833 

6-54 

3,728 

5-55 

3,244 

6.38 

72,763 

4.99 

43,944 

8.26 

5,958 

4.64 

3,735 

7.40 

115,076 

4.92 

62,233 

9. II 

30,946 

5 -oi 

23,680 

6-55 

10,833 

4.86 

8,260 

6.38 

8,772 

4-75 

8,246 

5-05 

11,406 

4-38 

6,552 

7-63 

4,834 

4 - 5 i 

3,725 

5-85 

96,992 

5-19 

61,069 

8.24 

52,025 

4.90 

28,017 

9.11 

32 ,H 3 

4.99 

27,181 

5 • S9 

9,396 

5-50 

8,527 

6 06 

6,076 

4.89 

4,792 

6.20 

4,544 

4.80 

4,342 

5-03 

8,106 

4-77 

6,990 

5-53 

5,945 

5-99 

5,279 

6-75 

4,359 

5 -i 4 

4,170 

5-37 

23,290 

5-oo 

20,493 

5-68 

4,281 

5.20 

3,874 

5 74 

5,332 

5-29 

4,308 

6-55 

4 , 43 i 

4.64 

3,8io 

5-39 

5,294 

5-24 

4,903 

5-66 

5,803 

5-05 

5,296 

5-53 

9,706 

5-04 

5,594 

8.75 

5,455 

4-93 

4,866 

5-52 

4.670 

4.76 

4,221 

5-27 

6,817 

4.70 

5,752 

5-57 

6,429 

4.78 

5,967 

5.16 

9 A 37 

4.60 

5-736 

7*32 

6,717 

4.62 

2.695 

11.50 

3,88i 

5-65 

2,084 

10.52 

15,650 

4.80 

13,727 

5-47 

23,957 

5-04 

14,049 

*•59 

9-347 

5-97 

8,609 

6.48 

5,379 

4-79 

5 A 33 

5.02 

7,488 

5-23 

4,608 

8.50 

24,343 

5 *08 

18,898 

6-55 

ii ,439 

5-20 

8,245 

7.21 

8,209 

4.66 

6,315 

6.06 

6,338 

5 -i 5 

3,589 

9.09 

7,943 

4-23 

7 A 74 

4.68 






























































STATISTICS OF HUNDRED AMERICAN CITIES. 


33 b 


Population, Etc., in Hundred American Cities.—( Continued ,.) 


CITIES. 

Size. 

Population. 

Families. 

Dwellings. 

Number. 

Persons to 
a lamily. 

Number. 

Persons 
to a 

dwelling. 

Milwaukee, Wis. 

19 

115,587 

23,024 

5-02 

18,748 

6.17 

Minneapolis, Minn.. 

38 

46,887 

8,584 

5-46 

6,932 

6.76 

Mobile, Ala. 

68 

29,132 

6,133 

4-75 

5,276 

5-52 

Nashville, Tenn. 

40 

43 350 

8,525 

5-09 

7,072 

6.13 

Newark, N. T. 

15 

136,508 

28,386 

4.81 

18,706 

7.26 

New Bedford, Mass.. 

75 

26,845 

6,147 

4-37 

5,038 

5-33 

New Haven, Conn.. . 

26 

62,882 

13,638 

4.61 

9,961 

6.31 

New Orleans, La. ... 

10 

216,090 

45,316 

4-77 

36,347 

5-95 

Newport, Ky. 

98 

20,433 

4, III 

4*97 

3,225 

6-34 

New York, N. Y... . 

1 

1,206,299 

243 T 57 

4.96 

73,684 

16.37 

Norfolk, Va. 

83 

24,966 

5,098 

4 - 3 i 

3,277 

6.70 

Oakland, Cal. 

5 i 

34.555 

7,018 

4.92 

6,416 

5-39 

Omaha, Neb. 

63 

30.518 

5,612 

5-44 

5,no 

5-97 

Oswego, N. Y. 

92 

21,116 

4,398 

4.80 

4 T 53 

5.08 

Paterson, N. J. 

34 

51,031 

10,679 

4.78 

6,712 

7.60 

Peoria, Ill. 

67 

29,259 

5,879 

4.98 

5,482 

5-34 

Petersburg, Va. 

89 

21,656 

4,779 

4-53 

3,426 

6.32 

Philadelphia, Pa. 

2 

847,170 

165,044 

5-13 

146,412 

5-79 

Pittsburg, Pa. 

12 

156.389 

29,868 

5-24 

24,289 

6.44 

Portland, Me. 

53 

33,8io 

7,295 

4-63 

5 T 57 

6.56 

Poughkeepsie, N. Y. 

99 

20,207 

4,302 

4.70 

3,403 

5-94 

Providence, R. I. 

20 

104,857 

23,178 

4-52 

I 4 U 53 

7.41 

Ouincy, Ill. 

73 

27,268 

5,532 

4-93 

4,715 

5-78 

Reading, Pa. 

4 i 

43,278 

8,876 

4.88 

8,267 

5-24 

Richmond, Va. 

25 

63,600 

12,180 

5.22 

9,532 

6.67 

Rochester, N. Y. 

22 

89,366 

18,039 

4-95 

15,825 

5-65 

Sacramento. Cal. 

9 ° 

21,420 

4,752 

4 - 5 i 

4,222 

5-07 

St. Joseph, Mo. 

57 

32 , 43 i 

5,630 

5-76 

5,260 

6.17 

St. Louis, Mo. 

6 

350,518 

65,142 

5-38 

43,026 

8.15 

St Paul. Minn. 

45 

41,473 

7,224 

5-74 

6,343 

6-54 

Salem, Mass. 

72 

27,563 

6,167 

4-47 

4,241 

6.50 

Salt Lake City, Utah. 

93 

20,768 

4,207 

4.94 

3,755 

5-53 

San Antonio, Texas.. 

96 

20,550 

3,864 

5-32 

3,632 

5.66 

San Francisco, Cal... 

9 

233,959 

43,463 

5-38 

34 ,no 

6.86 

Savannah, Ga. 

62 

30.709 

6,684 

4-59 

5,572 

5 - 5 i 

Scranton. Pa. 

39 

45,850 

8,926 

5 • T 4 

7,334 

6.25 

Somerville, Mass. . . 

78 

24.933 

5 , 4 W 

4.60 

4,106 

6.07 

Springfield, Ill. 

100 

19,743 

3 , 9 l6 

5-04 

3,525 

5.60 

Springfield, Mass... . 

55 

33-340 

7,368 

4-52 

5,033 

6.62 

Springfield, Ohio.... 

94 

20,730 

4.339 

4.78 

3,786 

5 ,48 

Syracuse, N. Y. 

32 

5 L 792 

11,046 

4.69 

8,825 

5-87 

Taunton, Mass. 

9 1 

21,213 

4,450 

4-77 

3,261 

6.51 

Terre Haute, Ind. .. . 

76 

26,042 

5,078 

5 -i 3 

4 , 58 i 

5.68 

Toledo, Ohio. 

35 

50,137 

10,191 

4.92 

9 , 7 W 

5 -i6 

Trenton, N. J. 

64 

29,910 

5,472 

5-47 

5 ,H 5 

5-85 

Troy, N. Y. 

29 

56,747 

11, 49 1 

4.94 

6,955 

8.16 

Utica, N. Y. 

52 

33 , 9 H 

6,996 

4-85 

5 , 8 i 5 

5 - S3 

Washington, D. C... 

14 

147,293 

29,603 

4.98 

24,107 

6.11 

Wheeling, W. Va. ... 

61 

30,737 

6,233 

4-93 

5 , 12 8 

5-99 

Wilkesbarre, Pa. 

79 

23,339 

4,424 

5.28 

4 U 57 

5.61 

Wilmington, Del. . . . 

42 

42,478 

8,243 

5 -i 5 

7,641 

5 • 56 

Worcester, Mass ... 

28 

58,291 

ii, 93 i 

4.89 

6,634 

8.79 




































































34 


QUANTITY OF WATER REQUIRED. 


10. Approximate Consumption of Water. — In 

American cities, having well arranged and maintained sys¬ 
tems of water supply, and furnishing good wholesome 
water for domestic use, and clear soft water adapted to the 
uses of the arts and for mechanical purposes, the average 
consumption is found to be approximately as follows, in 
United States gallons: 

(a.) For ordinary domestic use, not including hose use, 
20 gallons per capita per day. 

(b.) For private stables, including carriage washing, 
when reckoned on the basis of inhabitants, 3 gallons per 
capita per day. 

(c.) For commercial and manufacturing purposes, 5 to 
15 gallons per capita per day. 

(d.) For fountains, drinking and ornamental, 3 to 10 
gallons per capita per day. 

(e.) For lire purposes, ^ gallon per capita per day. 

{/.) For private hose, sprinkling streets and yards, 
10 gallons per capita per day, during the four dryest 
months of the year. 

(g.) Waste to prevent freezing of w T ater in service-pipes 
and house-fixtures, in Northern cities, 10 gallons per capita 
per day, during the three coldest months of the year. 

(Ji.) Waste by leakage of fixtures and pipes, and use 
for flushing purposes, from 5 gallons per capita per day 
upward. 

The above estimates are on the basis of the total popu¬ 
lations of the municipalities. 

There will be variations from the above approximate 
general average, with increased or decreased consumption 
for each individual town or city, according to its social and 
business peculiarities. 


WATER SUPPLIED TO ANCIENT CITIES. 


35 


The domestic use is greatest in the towns and cities, and 
in the portions of the towns and cities having the greatest 
wealth and refinement, where water is appreciated as a 
luxury as well as a necessity, and this is true of the yard 
sprinkling and ornamental fountain use, and the private 
stable use. 

The greatest drinking-fountain use, and fire use, and 
general waste, will ordinarily be in the most densely- 
populated portions, while the commercial and manufactur¬ 
ing use will be in excess where the steam-engines are most 
numerous, where the hydraulic elevators and motors are, on 
the steamer docks, and wdiere the brewing and chemical 
arts are practiced. 

The ratio of length of piping to the population is greater 
in wealthy suburban towns than in commercial and manu¬ 
facturing towns. 

Some of these peculiarities are brought out in a follow¬ 
ing table of the quantity of water supplied and of piping in 
several cities, which is based upon the census table hereto¬ 
fore given and upon various w T ater-works reports for the 
year 1870. 

The general introduction of public water-works, on the 
constant-supply system, with liberal pressures in the mains 
and house-services, throughout the American towns and 
cities, has encouraged its liberal use in the households, so 
that it is believed that the legitimate and economical domes¬ 
tic use of water is of greater average in the American cities 
than in the cities of any other country, at the present time, 
and its general use is steadily increasing. 

11. Water Supplied to Ancient Cities.— The sup¬ 
plies to ancient Jerusalem, imperial Rome, Byzantium, and 
Alexandria, were formerly equal to three hundred gallons 
per individual daily ; and, later, the supplies to Nismes, 


36 


QUANTITY OF WATER REQUIRED. 


Metz, and Lyons, in France, and Lisbon, Segovia, and 
Seville, in Spain, were most liberal, but a small proportion 
only of the water supplied from these magnificent public 
works was applied to domestic use, except in the palaces 
of those attached to the royal courts. 

12. Water Supplied to European Cities. —In the 
year 1870, the average daily supply to some of the leading 
European cities was approximately as follows : 


CITIES. 


Imp. Gallons. 


London, England . 
Manchester, “ 
Sheffield, “ 
Liverpool, “ 
Leeds, “ 

Edinburgh, Scotland 
Glasgow, “ 

Paris, France ... 
Marseilles, “ .... 

Genoa, Italy. 

Geneva, Switzerland 

Madrid, Spain. 

Berlin, Prussia. 


2 9 

24 

2 9 
2 7 
2 3 

30 

40 

30 

40 

3 ° 

16 

16 

18 


In the year 1866, public water supplies * were, in vol¬ 
ume, as follows, in the cities named : 


CITIES. 

Population. 

Supply per Capita. 

Hamburg, Prussia. 

200,000 

52,000 

42,000 

53 , 000 
100,000 

I 12,000 
300,000 

34 gals. 

20 “ 

22 “ 

II -5 “ 

* 3-5 

i?.6 u 

22 “ 

Altona, “ . 

Tours, France. 

Angers, “ . 

Toulouse, “ ... . 

Nantes, “ . 

Lyons, “ . 


* Vide Kirkwood’s “ Filtration of River Waters.” Van Xostrand, N. Y., 1869. 











































WATER SUPPLIED TO AMERICAN CITIES. 


n -v 

c i 


Prof. Rankine gives, * as a fair estimate of the real daily 
demand for water, per inhabitant, amongst inhabitants of 
different habits as to the quantity of water they consume, 
the following, based upon British water supply and con¬ 
sumption : 


Rankine’s Estimate for England. 



Imp. Gallons per 

Day. 


Least. 

Average. 

Greatest. 

Used for domestic purposes. 

Washing streets, extinguishing fires, sup- 

7 

IO 

15 

plying fountains, etc. 

3 

3 

3 

Trade and manufactures. 

7 

7 

7 

Waste under careful regulations, say.. .. 

2 

2 

2 1 
z 2 

Total demand. 

J 9 

22 

2 7 i 


13. Water Supplied to American Cities. —The lim¬ 
ited use of water for domestic purposes in many of the 
European cities during the last half century, led the engi¬ 
neers who constructed the pioneer water-works of some of 
the American States to believe that 30 gallons of water per 
capita daily would be an ample allowance here; and in 
their day there was scarce a precedent to lead them to 
anticipate the present large consumption of water for lawn 
and street sprinkling by hand-hose, or for waste to prevent 
freezing in our Northern cities. 

The following tables will show that this early estimated 
demand for water has been doubled, trebled, and in some 
instances even quadrupled; and this considerable excess, 
to which there are few exceptions, has been the cause of 
much annoyance and anxiety. 


* “ Civil Engineering,” London, 1872, p. 731. 


















38 


QUANTITY OF WATER REQUIRED. 


In the year 1870, the average daily supply to some of 
the American cities was as follows, in United States gallons : 

TABLE No. 2. 

Water Supplied and Piping in Several Cities, in the year 1870? 


CITIES. 

Popula¬ 
tion 
in 1870. 

Supply 

per 

Person, 

Daily 

Average 

Supply 

per 

Family, 

Daily 

Average. 

Supply 

per 

Dwelling, 

Daily 

Average. 

Total 

Daily Supply, 
Average. 

Total Miles 

of Pipe Mains. 

Miles of Pipe 

PER 1,000 

Inhabitants. 



Gallons . 

Gallons . 

Gallons . 

Gallons . 

Miles . 

Miles . 

Baltimore.... 

267,354 

52.8l 

282.53 

35°* I 3 

14,122,032 

2 14 

0.80 

Boston . 

25°,526 

60.15 

3 I2 -7 8 

5 o8 * 8 7 

15,070,400 

I94 

O.78 

Brooklyn .... 

396,099 

47.r6 

233-44 

407.46 

18,682,2 19 

25 8 

O.65 

Buffalo. 

117,74 

58.08 

306.08 

374*04 

6,838,303 

56 

O.48 

Cambridge.. . 

39,634 

43-9° 

220.38 

273*94 

1,739, 8 69 

60 

I.64 

Charlestown. . 

28,323 

43-9° 

201.94 

282.72 

1,243,38° 

25 

O.9O 

Chicago. 

298,977 

62.32 

3i3*47 

4i7*54 

18,633,000 

24O 

O.81 

Cincinnati .. . 

216,239 

40.00 

201.60 

35 2 *4o 

10,812,609 

132 

0.6l 

Cleveland.... 

92,829 

33*24 

,67-53 

184.81 

3.085.559 

5° 

°*54 

Detroit. 

79,577 

64.24 

236.98 

348.18 

5, 112 ,493 

129 

i.61 

Hartford. 

37480 

65.81 

329-7, 

365*9° 

2,447,00° 

48 

1.30 

Jersey City. .. 

82,546 

83.66 

414.12 

700.23 

6,906,056 

70 

0.85 

Louisville.... 

ioo,753 

28.95 

,51-99 

198.89 

2,817,300 

58 

0.58 

Montreal, Can. 

117,500 

49.00 

• • • • • • 

• •••••• 

5,720,306 

96 

0.81 

Newark. 

105,059 

20.20 

9 8 * t 7 

147.86 

2,121,842 

52 

0.50 

New Haven.. 

50,840 

59.00 

286.15 

37o*52 

.3,000,000 

53 

1.04 

New Orleans . 

i9L4i8 

30.1.9 

!47* 6 3 

171.78 

5.779.3,7 

58 

0.30 

New York .. . 

942,292 

90.20 

457-3, 

[1,327.74 85,000,000 

346 

°*37 

Philadelphia . 

674,022 

55- 11 

290.98 

33 1 * 21 

37, 1 45,385 

488 

0.71 

Salem. 

24,117 

4I.46 



1,000,000 

35 

104 


. 



St. Louis .... 

310,864 

35-38 

| 185.04 

277.38 

11,000,000 

io 5 

°*34 

Washington.. 

109,199 127.00 

650.24 

709.93 

13,868,273 

102 

°*93 

Worcester. . .. 

41405 

48.65 

230.60 

406.23 

2,000,000 

45 

1.09 


The average quantity of water supplied to some of the 
1 same cities in 1874 is indicated in the following table, show¬ 
ing also the extensions of the pipe systems, and the increase 
in the average daily consumption of water per capita, from 
year to year: 


* See also statistics on page 609. 


























































INCREASE IN VARIOUS CITIES. 


30 


TAB LE No. 3. 


Water Supplied in Years 1870 and 1874. 


CITIES. 

Average 
Daily Supply 
per Capita. 

Total Average Daily Supply. 

Total 

Miles of Pipes. 

1870. 

1 

1874. 

1870. 

1874. 

1870. 

iS: 4 - 

Boston. 

60 

60 

i 55 ° 7 °) 4 00 

18,000,000 

194 

262 

Brooklyn. 

47 

58 

18,682,219 

24,772,467 

258 

323 

Buffalo.. 

ss 

60 

6,838,303 

8,509,481 

56 

87 

Cambridge. 

44 

54 

739 ,869 

2,300,000 

60 

76 

Charlestown ... 

44 

62 

1,243,380 

7,643,017 

25 

132 

Chicago. 

64 

84 

18,633,000 

38,090,952 

240 

386 

Cincinnati. 

40 

45 

10,812,609 

x 3,600,596 

132 

x 5 6 

Cleveland. 

32 

45 

3,085,559 

5,625,15° 

5 ° 

81 

Detroit. 

64 

87 

5, ii2 ,493 

9 , OI 3 , 35 ° 

129 

x 77 

Jersey City. 

84 

86 

6,906,056 

10,421,001 

7 ° 

hi 

Louisville. 

29 

24 

2,817,300 

3 , 598,730 

58 

9 1 

Newark. 

20 

38 

2,121,842 

4 , 73 2 , 7 l8 

52 

112 

Philadelphia .. . 

55 

58 

37 , t 45 , 3 8 5 

42,111,730 

488 

625 

Salem. 

41 

55 

1,000,000 

1,380,000 

35 

40 

Washington .... 

127 

138 

13,868,273 

18,000,000 

102 

141 

Worcester. 

49 

80 

2,000,000 

3,000,000 

45 

63 

Montreal. 

49 

66 

5,720,306 

8,395,8io 

96 

114 


14. The Use of Water Steadily Increasing-.— The 

legitimate use of water is steadily being popularized, calling 
for an increased average in the amount of household appa¬ 
ratus, increased facilities for garden irrigation and jets 
d’eau, increased street areas moistened in dusty seasons, 
and increased appliances for its mechanical use; from all 
which follows increased waste of water. 

15. Increase in Various Cities. —The following table 
is introduced to show the average daily supply in various 
cities through a succession of years: 











































40 


QUANTITY OF WATER REQUIRED. 


TABLE No. 4. 

Average Gallons Water Supplied to Each Inhabitant Daily in 














.d 

3 

d 

0 

YEAR. 

fl 

O 

6 

d 

>> 

3 

•O 

a 

a 

0 

a 

c 

0 

4-» 

O 

G 

>> 

t > 
c n 

<D 

U 

u 

O 

Oh 

JO. 

•a 

fcJD 

_a 

3 


-*-» 

C /3 

O 

£ 

3 

O 

O 

Ih 

> 

fl 

O 

• l-H 

40 

u 

-+-> 

<u 

<73 

U 

3 

0 

c 

0 

£ 

3 

cn 

03 


03 

03 

03 

0 

G 

O 

Q 

'—> 



£ 

Oh 

> 

i8c6 ... . 
i8 57 . 

— 

— 

— 

8 

— 

— 

55 

46 

— 

— 

— 

— 

— 

— 

i8 5 8 . 

— 

— 

— 

8 

— 

33 

46 

75 

— 

— 

— 

— 

— 

^59 . 

— 

— 

— 

11 

— 

4 ° 

4 8 

— 

— 

— 

— 

— 

— 

i860 .... 

— 

— 

— 

14 

— 

43 

5 2 

77 

— 

— 

— 

— 

— 

l 86 l . 

— 

— 

— 

16 

— 

43 

53 

— 

9 

— 

— 

— 

— 

l862 . 

— 

— 

J 7 

J 9 

39 

44 

58 

— 

14 

— 

— 

— 

— 

I 8 63 . 

— 

— 

22 

21 

— 

43 

58 

— 

12 

— 

— 

— 

— 

1864 . 

— 

— 

26 

22 

— 

4 i 

57 

— 

14 

— 

62 

— 

— 

i8 ^5 . 

— 


29 

22 

— 

42 

55 

77 

*7 

— 

— 

— 

— 

1866. 

55 

— 

33 

22 

— 

43 

60 

— 

17 

— 

— 

— 

— 

1867 . 

59 

— 

36 

24 

— 

5 ° 

64 

— 

15 

— 

62 

46 

— 

1868 . 

62 

— 

43 

2 5 

— 

58 

67 

— 

16 

— 

68 

5 1 

— 

1869 . 

62 

— 

46 

27 

— 

62 

61 


18 

— 

84 

5 1 

— 

1870 . 

60 

58 

47 

33 

40 

63 

64 

84 

29 

49 

90 

55 

127 

1871 ».... 

54 

5 1 

46 

36 

— 

73 

73 


J 9 

55 

85 

55 

130 

1872 . 

55 

61 

5 ° 

40 

60 

75 

8 3 

99 

22 

55 

88 

54 

J 34 

i8 73 . 

58 

60 

55 

43 

— 

75 

90 


22 

60 

104 

56 

138 

i8 74 . 

60 

60 

58 

45 

45 

8 4 

8 7 

86 

2 4 

66 

— 

58 

138 

1882 . 

99 

106 

55 

65 

76 

114 

149 

124 

5 2 

66 

79 

66 

176 


16. Relation of Supply per Capita to Total Pop¬ 
ulation.— In the larger cities there are generally the great¬ 
est variety of purposes for which water is required, and 
consequently a greater average daily consumption per cap¬ 
ita. Exceptions to this general rule may be found in a few 
suburban towns largely engaged in the growth of garden 
truck, and plants, and shrubs for the urban markets, in 
which there is a large demand for water for purposes of 
irrigation. 

In the New England towns and cities the average daily 
consumption and waste of water according to population is 
approximately as follows: 























































MONTHLY AND HOURLY VARIATIONS. 


41 


Places of 10,000 population, 35 to 45 gallons per capita. 

“ “ 20,000 “ 40 to 50 “ “ “ 

“ “ 30,000 “ 45 to 65 “ “ “ 

“ “ 50,000 “ 55 to 75 “ “ “ 

Places of 75,000 population and upward, 60 to 100 gal¬ 
lons per capita. 

17. Monthly and Hourly Variations in t-lie Draught. 

—The data heretofore given relating to the daily average 
consumption of water have referred to annual quantities 
reduced to their daily average. The daily draught is not, 
however, uniform throughout the year, hut at times is 
greatly in excess of the average for the year, and at other 
times falls below. 

# 

It may be twenty to thirty per cent, in excess during 
several consecutive weeks, fifty per cent, during several 
consecutive days, and not infrequently one hundred per 
cent, in excess during several consecutive hours, independ¬ 
ently of the occasional heavy drafts for fires. Diagrams of 
this daily consumption of water in the cities usually show 
two principal maxima and two principal minima. The 
earliest maximum in the year occurs, in the Eastern and 
Middle States, about the time the frost is deepest in the 
ground and the weather is coldest, that is, between the 
middle of January and the first of March, and in New 
England cities this period sometimes gives the maximum of 
the year. The second maximum occurs usually during the 
hottest and dryest portion of the year, or between the mid¬ 
dle of July and the first of September. The two principal 
minima occur in the spring and autumn, about midway 
between the maxima. Between these four periods the pro¬ 
file shows irregular wavy lines, and a profile diagram 
continued for a series of years shows a very jagged line. 

To illustrate the irregular consumption of water, we 


1871 1 8 7 2 /#73 / R7 f \ / 

J F MAM tT <TAS O ND JF.MAMJ J A S 0 NT) JFMAMJJ/IS O ND JFMAMJ iJ /I S (AMD 




•saStfWAB Amiuoj\[ 'uiaip aad suo[[b3 uojuiux jo 'Ofg; 



























































































































































































































































































































































RATIO OF MONTHLY CONSUMPTION. 


43 


have prepared the diagrams, Fig. 1, of the operations of the 
pumps at Chicago, Brooklyn, Cincinnati, and Montreal, 
during the years 1871, 1872, 1873, and 1874. 

18. Ratio of Monthly Consumption. —The varia¬ 
tions in draught, as by monthly classification, in several 
prominent cities, in the year 1874, have been reduced to 
ratios of mean monthly draughts for convenience of compar¬ 
ison, and are here presented ; unity representing the mean 
monthly draught for the year: 


TABLE No. 5. 

Ratios of Monthly Consumption of Water in 1874. 


CITIES. 

C 

Feb. 

March. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

O 

O 

Nov. 

Dec. 

Brooklyn.... 

1.029 

1.132 

.971 

.892 

.941 

I 008 

1.069 

I.034 

I.044 

.987 

• 9 T 9 

•974 

Buffalo. . . 

1.008 

I.007 

.960 

.941 

•983 

• 9 6 3 

.996 

1.020 

I.044 

I.OII 

1.040 

I. COO 

Cleveland... 

.883 

.901 

.850 

.871 

.992 

I.180 

1.181 

1.206 

I.058 

I.OOI 

.942 

•915 

Detroit. 

.856 

.807 

• 9°5 

.844 

I.029 

I.065 

1.051 

I.167 

I-I 7 I 

1.115 

.987 

1.003 

Philadelphia. 

.850 

.844 

•834 

.898 

I.056 

UI99 

1.289 

I-I 45 

I.09I 

.990 

•952 

.853 

Chicago .... 

.862 

.844 

• 9°4 

.904 

.942 

.942 

1.171 

1193 

I.162 

1.039 

.966 

1.029 

Cincinnati... 

.792 

.762 

.778 

.856 

i.on 

I.2I7 

1.207 

1-257 

I.302 

1.058 

.960 

•799 

Louisville. .. 

.842 

.819 

.848 

.841 

.960 

1.192 

1.207 

1.223 

1.202 

1.138 

.940 

.C76 

Montreal.... 

.864 

•959 

•943 

I.025 

.916 

• 9°7 

I.IOI 

1.151 

I.O96 

1.043 

.971 

1.023 

Mean... 

.887 

.897 

.888 

.897 

.960 

1-075 

1.144 

1 .155 

I.I30 

1.042 

.964 

.941 


There is also a very perceptible daily variation in each 
week, and hourly variation in each day, in the domestic 
consumption of water. 

The Brooklyn diagram shows that the average draught 
in the month of maximum consumption was in 1872, fifteen 
per cent, in excess of the average annual draught; in 1873, 
seventeen per cent, in excess ; in 1874, thirteen per cent, in 

excess. 

A Boston Highlands direct pumping diagram lying be¬ 
fore the writer shows that the average draught at nine 
o’clock in the forenoon was thirty-seven per cent, in excess. 











































♦ 


























CHAPTER III. 


RAINFALL. 

21. The Vapory Elements. —The elements of water 
fill the ethereal blue above and the earth crust beneath. 
They, with unceasing activity, permeate the air, the rocks, 
the sand, the fruits we eat, and the muscles that aid our 
motion. 

Since hrst £C there went up a mist from the earth,” the 
struggle between the ethereal elements and earth’s internal 
tire, between the intense cold of space and direct and 
radiated heat enveloping the face of the earth, has gone 
on unceasingly. 

22. The Liquid and Gaseous Successions. —If we 
hold a drop of water in the clear sunshine and watch it 
intently, soon it is gone and we could not see if depart; if 
we expose a dish of water to the heat of tire, silently it 
disappears, and we know not how it gathered in its activity; 
if we leave a tank of water uncovered to the sun and wind, 
it gradually disappears, and is replenished by many showers 
of summer, still it departs and is replenished by snows of 
winter. Under certain extreme conditions it may never be 
full, it may never be exhausted, the rising vapor may equal 
the falling liquid, as where “ the rivers flow into the sea, yet 
the sea is not full.” 

23. The Source of Showers. —Physical laws whose 
origin we cannot comprehend but whose steady effects we 
observe, lift from the saline ocean, the fouled river, the moist 
earth, a stream of vapor broad as the circuit of the globe, 


46 


RAINFALL. 


but their solid impurities remain, and the flow goes up with 
ethereal clearness. 

From hence are the sources of water supply replenished. 
From hence comes the showers upon the face of the earth. 

24. General Rainfall. —But there is irregularity in 
the physical features of the earth, and unevenness in the 
temperature about it, and the showers are not called down 
alike upon all its surface. Upon the temperate zone in 
America enough water falls in the form of rain and snow 
to cover the surface of the ground to an average depth of 
about 40 inches, in the frigid zone a lesser quantity, and in 
the torrid zone full 90 inches, and in certain localities to 
depths of 100 and 150, and at times to even 200 inches. 

We recognize in the rain an ultimate source of water 
supply, but the immediate sources of local domestic water 
supply are, shallow or deep wells , springs , lakes , and rivers . 
The amplitude of their supply is dependent upon the avail¬ 
able amount of the rainfall that replenishes them. In 
cases of large rivers, and lakes like the American inland 
seas, there‘can be no question as to their answering all 
demands, as respects quantity, that can be made upon them, 
but often upon watersheds of limited extent, margins of 
doubt demand special investigations of their volumes of 
rainfall, and the portions of them that can be utilized. 

25. Review of Rainfall Statistics. —Looking broadly 
over some of the principal river valleys of the United States 
we find their average annual rainfalls to be approxi¬ 
mately as follows : Penobscot, 45 inches ; Merrimack, 43 ; 
Connecticut, 44 ; Hudson, 39 ; Susquehanna, 37 ; Roanoke, 
40; Savannah, 48; Appalacliicola, 48; Mobile, 60; Mis¬ 
sissippi, 46 ; Rio Grande, 19 ; Arizonian Colorado, 12 ; Sac¬ 
ramento, 28 ; and Columbia, 33 inches ; but the amount 
of rainfall at the various points from source to mouth of 



WESTERN RAIN SYSTEM. 


47 


each river is by no means uniform ; as, for instance, upon 
the Susquehanna it ranges from 26 to 44 inches; on the 
[ Rio Grande, from 8 to 87 inches ; and on the Columbia, 
from 12 to 86 inches. 

26. Climatic Effects. —The North American Continent 
presents, in consequence of its varied features and reach 
from near extreme torrid to extreme polar regions, almost 
all the special rainfall characteristics to be found upon the 
face of the globe; and even the United States of America 
includes within its limits the most varied classes of climato¬ 
logical and meteorological effects, in consequence of its range 
of elevation, from the Florida Keys to the Rocky Mountain 
summits, and its range of humidity from the sage-bush 
plains between the Sierras and Wahsatch Mountains, and 
the moist atmosphere of the lower Mississippi valley, and 
from the rainless Yuma and Gila deserts of southern Cali¬ 
fornia to the rainy slopes of north-western California and of 
Oregon, where almost daily showers maintain eternal verdure. 

27. Sections of Maximum Rainfall.— The maxi¬ 
mum recorded rainfall, an annual mean of 86 inches, occurs 
in the region bordering upon the mouth of the Columbia 
River and Puget Sound. A narrow belt of excessive hu¬ 
midity extends along the Pacific coast from Vancouver’s 
Island southerly past the borders of Washington Territory, 
Oregon and California, to latitude 40°. 

Next in order of humidity is the region bordering upon 
the Delta of the Mississippi River and the embouchure of 
the Mobile, whose annual mean of rain reaches 64 inches. 

Next in order is a section in the heart of Florida of 
about one-half the breadth of the State, whose mean annual 
rain reaches 60 inches. 

28. Western Rain System.— The great northerly 
ocean current of the Pacific moves up past the coast of 


48 


RAINFALL. 


China and the Aleutian Islands and impinges upon the 
North American shore, then sweeps down along the coast 
of Washington Territory, Oregon and California ; and from 
its saturated atmosphere, flowing up their bold western 
slopes, is drawn the excessive aqueous precipitations that 
water these regions. 

Their moist winds temper the climate and their condensed 
vapors irrigate the land, so that the southerly portion of the 
favored region referred to is often termed the garden of 
America. 

Fig. 2 is a profile, showing a general contour across the 
North American Continent, along the thirty-ninth parallel 
of latitude. 


Fig. 2. 
E 



Elevation. 

feet . 


A. Pacific Ocean. a . Sacramento City. 82 

B. Coast Range. b. Carson City. 4,629 

C. Sierra Nevada. c . Salt Lake Region. 41382 

D. Wahsatch Mountains. d. Colorado River. — 

E. Rocky Mountains. e . Colorado City. 6,000 

F. Mississippi River. f. St. Louis. 481 

G. Alleghany Mountains. g. Cincinnati. 582 

H. Blue Ridge. h. Washington.. 70 

I. Atlantic Ocean. 


The California coast range and the western slope of the 
Sierra Nevadas are the condensers that gather from the 
prevailing westerly ocean breezes their moisture. From 
thence the winds pass easterly over the Sierra summit 
almost entirely deprived of moisture, and yield but rarely 
any rain upon the broad interior basin stretching between 
the bases of the Sierra and Wahsatch Mountains. Upon the 













CENTRAL RAIN SYSTEM. 


49 


arid plains of this region, above the Gulf of California, 
whose average annual rainfall reaches scarce 4 inches, the 
winds roll down like a thirsty sponge. 

Further to the east, the western slopes of the Walisatcli 
and Rocky Mountains lift up and condense again the west¬ 
ern winds, and gather in their storms of rain and snow. 
In the lesser valley between these mountains, 12 to 20 
inches of rain falls annually, and the tributaries of the, 
Colorado River gathers its scanty surplus of waters and 
leads them from thence around the southerly end of the 
Walisatcli Mountains past the Yuma Desert to the Gulf. 

Over the summit of the Rocky Mountains onward moves 
the westerly wind, again deprived of its vapor, and down it 
rolls with thirsty swoop upon the Great American Desert, 
skirting the eastern base of the mountains. Farther on, it 
is again charged with moisture by the saturated wind-eddy 
from the Caribbean Sea and Gulf of Mexico. 

The great Pacific currents of water and wind, and the 
extended ridges and furrows of the westerly half of our 
Continent lend their combined influence, in a marked man¬ 
ner, to develop its special local and its peculiar general 
climatic and meteorological systems. 

29. Central Rain System.— A second system of anti¬ 
trade winds bears the saturated atmosphere of the Gulf of 
Mexico up along the great plain of the Mississippi. Its 
moisture is precipitated in greatest abundance about the 
delta, and more sparingly in the more elevated valleys of 
the Red and Arkansas rivers upon the left, and the Tennes¬ 
see and Ohio rivers upon the right. Its influence is per¬ 
ceptible along the plain from the Gulf to the southern bor¬ 
der of Lake Michigan, and easterly along the lower lakes 
and across New England, where the chills of the Arctic 
polar current sweeping through the Gulf of St. Lawrence 
4 


50 


RAINFALL. 


and down the Nova Scotia coast into Massachusetts Bay, 
throws down abundantly its remaining moisture. 

30. Eastern Coast System. — A third system en¬ 
velops Florida, Georgia, and the eastern Carolinas, espe¬ 
cially in summer, with an abundance of rain. 

A fourth subordinate system shows the contending 
thermic and electric influences of the warm and moist 
atmosphere from the Gulf Stream, flowing northerly past, 
and of the cooler atmosphere from the polar current flowing 
southerly upon the New England coast, where an abundant 
rain is distributed more evenly throughout the seasons than 
elsewhere upon the Continent. 

31. Influence of Elevation upon Precipitation.— 

The influence of elevation above the sea-level is far less 
active in producing excessive rain upon our mountain 
ranges and high river sources than upon other continents 
and some of the mountainous islands, being quite subordi¬ 
nate to general wind currents. 

Upon the mountainous island of Guadaloupe, in latitude 
16°, for instance, a rainfall of 292 inches per annum at an 
elevation of 4500 feet is recorded. 

Upon the Western Ghauts of Bombay, at an elevation 
of 4,500 feet, an average rainfall for fifteen years is given as 
254 inches. 

On the southerly slope of the Himalayas, northerly of 
the Bay of Bengal, at an elevation of 4,500 feet, the rainfall 
of 1851 was 610 inches. These localities all face prevailing 
saturated wind currents. 

32. River-basin Rains. — A study of some of our 
principal river valleys independently, reveals the fact that 
their rainfall gradually decreases from their outlets to their 
more elevated sources. 


RIVER-BASIN RAINS. 


51 


In illustration of this fact, we present the following* river- 
valley statistics relating to the principal basins along the 
Atlantic, Gulf, and Pacific coasts. 


TABLE No. 6. 

Mean Rainfall Along River Courses, showing the Decrease 
in Precipitation of Rain and Melted Snow from the 
River Mouths, upward. 


ST. JOHN’S RIVER. 


Name of Station. 

Summer. 

Winter. 

Y EAR. 

Distance from Mouth. 


St. Johns. 

Fort Kent. 

Inches. 

IO 

12 

Inches. 

14 

IO 

Inches. 

5 i 

36 

Miles ( approximate). 

5 ) Distances from 
oorv r the Atlantic 
2 3 ° > Ocean. 

Average rain, 
43 inches. 


MERRIMACK RIVER. 


Newburyport. 

12 

12 

4i 

51 

Lawrence. 

19 

11 

45 

25 

Manchester. 

11 

11 

45 

60 

Concord. 

11 

9 

4i 

78 J 


Distances from 
the Atlantic 
Ocean. 


Average rain, 
43 inches. 


CONNECTICUT RIVER. 


Sa)'brook ... 
Middletown.. 

Hartford. 

Hanover. 

St. Johnsbury 


13 • 

13 

49 

4 ' 

13 

12 

46 

25 

IO 

11 

44 

40 ► 

11 

9 

40 

180 

11 

8 

36 

235 . 


Distances from 
Long Island 
Sound. 


Average rain, 
44 inches. 


HUDSON RIVER. 


New York City. 

12 

IO 

44 

8 1 

Poughkeepsie. 

12 

9 

40 

75 l 

Hudson. 

IO 

7 

35 

115 

Albany. 

9 

8 

36 

145 J 


Distances from 
the Atlantic 
Ocean. 


Average rain, 
39 inches. 


SUSQUEHANNA RIVER. 


Havre de Grace .... 

13 

IO 

44 

5 ] 

Harrisburg. 

12 

8 

49 

70 

Lewisburg. 

11 

8 

39 

120 1 

Williamsport. 

IO 

7 

39 

140 

Owego. 

8 

6 

34 

200 

Elmira. 

7 

4 

26 

200 J 


Distances from 
Chesapeake 
Bay. 


Average rain, 
37 inches. 




























































52 


RAINFALL. 


Mean Rainfall Along River Courses—( Continued ). 

MISSISSIPPI RIVER. 


Name of Station. 

Summer. 

W INTER. 

Year. 

Distance from Mouth. 


Inches. 

Inches. 

Inches. 

Miles (approximate). 

Delta. 

20 

18 

60 

IO' 


New Orleans. 

20 

16 

60 

95 


Baton Rouge. 

18 

15 

60 

190 


June, of Red River . . 

14 

16 

56 

240 


Vicksburg. 

II 

15 

55 

350 

Distances from 

Memphis. 

8 

15 

42 

560 

>- the Gulf of 

Cairo. 

11 

12 

42 

700 

Mexico. 

St. Louis. 

13 

8 

42 

850 


Dubuque . 

14 

5 

38 

1100 


Lacrosse. 

11 

3 

30 

1200 


St. Paul’s. 

11 

3 

25 

1500J 



.Average rain, 
46 inches. 


Brownsville. 

June. Pecos River .. 

El Paso. 

Albuquerque. 


8 

5 

4 

3 


RIO GRANDE. 


6 

3 

2 

2 


37 

18 

12 

8 


30 
400 
800 
1050 J 


Distances from 
the Gulf of 
Mexico. 


Average rain, 
19 inches. 


COLUMBIA RIVER. 


Astoria. 

4 

44 

86 

5 ") 



Walla-Walla. 

2 

5 

20 

275 

Distances from 

Average rain. 

Boise City. 

2 

7 

13 

600 

r the 

Pacific Ocean. 

33 inches. 

Fort Hall. 

• 

1 

6 

12 

CO 

cn 

O 

v 




Reference to the above, from among the principal river 
valleys, is sufficient to show that the oft-made statement, 
that “rain falls most abundantly on the high land,” is 
applicable, in the United States, to subordinate watersheds 
only, and in rare instances. 

33. Grouped Rainfall Statistics.— The following 
table gives the minimum, maximum, and mean rainfalls, 
according to the most extended series of observations, at 
various stations in the United States. They are grouped by 
territorial divisions, having uniformity of meteorological 
characteristics. 















































RAINFALL IN THE UNITED STATES. 


53 


TABLE No. 7. 


Rainfall in the United States. 

(.From Records to 1866 inclusive .) 

GROUP 1.—Atlantic Sea-coast from Portland to Washington. 


Station. 

Lat. 

Long. 

Height 

above 

Sea. 

Years 

of 

Record 

Min. 

Annual 

Rain. 

Max. 

Annual 

Rain. 

Mean 

Annual 

Rain. 






Inches. 

Inches. 

Inches. 

Gardiner, Me. 

44°10' 

69°46' 

76 

27 

30.19 

5i-47 

42.09 

Brunswick “ . 

43 54 

69 57 

74 

32 

26.38 

75.64 

44.68 

Worcester, Mass. 

42 16 

7i 49 

528 

26 

34.60 

61.83 

46 92 

Cambridge, “ .. 

42 23 

71 07 

71 

31 

30.04 

59-34 

46.39 

Boston, “ . 

42 22 

71 04 

.... 

28 

27.20 

67.78 

44-99 

New Bedford “ . 

41 39 

70 56 

90 

54 

30.68 

58.14 

41.42 

Providence, R. I . 

41 50 

71 23 

150 

35 

3°-5i 

54-17 

41-54 

Flatbush, N. Y . 

4° 37 

74 02 

54 

36 

32.14 

58.92 

43-52 

Fort Hamilton, “ . 

40 36 

74 02 

25 

19 

29-75 

62.69 

42.55 

Fort Columbus, “ . 

40 41 

74 01 

23 

24 

27.57 

65-51 

43-24 

New York City, “ . 

40 43 

74 00 

50 

3i 

34-79 

62.87 

43.00 

West Point, “ . 

41 24 

73 57 

167 

20 

35-05 

63-56 

47-65 

Newark, N. J. 

40 45 

74 10 

35 

23 

34-54 

57-05 

44-85 

Lambertville, “ . 

40 23 

74 56 

9 6 

17 

32.33 

57-37 

43-99 

Philadelphia, Penn. 

39 57 

75 n 

60 

43 

29-57 

62.94 

44-05 

Baltimore, Md. 

Fort McHenry, “ . 

Washington, D. C. 

39 18 

76 37 

«... 

28 

28.75 

62.04 

42.33 

39 16 

76 34 

36 

23 

22.87 

51-50 

41.10 

38 54 

77 °3 

no 

28 

23.24 

53-45 

37-52 

43-44 


GROUP 2.—Atlantic Sea-coast, Virginia to Florida. 


Fortress Monroe, Va. 

Charleston, S. C. 

Fort Moultrie, “ . 

Savannah, Ga. 

Fort Brooke, Fla. 


37°oo / 

7 6°i8' 

8 

32 47 

79 56 

25 

32 46 

79 5i 

25 

32 05 

81 05 

42 

28 00 

82 28 

20 


19 

19.32 

74-io 

47.04 

12 

23.69 

56.16 

43-63 

17 

33-98 

65-31 

45-51 

23 

25.98 

69-93 

48.32 

17 

35-93 

89.86 

53.63 




47-63 


GROUP 3.—Hudson River Valley, Vermont, Northern and Western 


Newburgh, N. Y . 

Poughkeepsie, “ . 

Kingston, “ . 

Hudson, “ . 

Kinderhook, “ . 

Albany, “ . 

Watervliet Arsenal, “ . 

Lansingburg, “ . 

Granville, “ . 

Hanover, N. H. 

Burlington, Vt. 

Fairfield, N. Y. 

Clinton, “ . 

Utica, “ . 

Lowville, “ . 

Gouverneur, “ . 

Potsdam, “ . 

Cazenovia, “ . 

Oxford, “ . 

Pompey, “ . 

Auburn “ . 

Ithaca, “ . 

Geneva, “ . 

Penn Yan, “ . 

Rochester, “ . 

Middlebury, “ . 

Fredonia, “ . 


New York. 


4i 

>3i' 

74 

’05' 

150 

20 

4i 

4i 

73 

55 

• • • • 

i5 

4i 

55 

74 

02 

188 

19 

42 

13 

73 

46 

150 

15 

42 

22 

73 

43 

125 

17 

42 

39 

73 

44 

130 

28 

42 

43 

73 

43 

50 

17 

42 

47 

73 

40 

3° 

20 

43 

20 

73 

17 

250 

15 

43 

42 

72 

17 

53° 

19 

44 

29 

73 

11 

346 

27 

43 

05 

74 

55 

1185 

17 

43 

00 

75 

20 

1127 

19 

43 

07 

75 

13 

473 

22 

43 

46 

75 

32 

847 

22 

44 

25 

75 

35 

400 

24 

44 

40 

75 

01 

394 

20 

42 

55 

75 

46 

1260 

25 

42 

28 

75 

32 

961 

20 

42 

56 

76 

05 

1300 

16 

42 

55 

76 

28 

650 

22 

42 

27 

76 

37 

4i7 

19 

42 

53 

77 

02 

567 

19 

42 

42 

77 

11 

740 

3° 

43 

08 

77 

5i 

516 

35 

42 

49 

78 

10 

800 

17 

42 

26 

79 

24 

710 

16 


25.04 

55.63 

36.61 



40.36 


• • • • 

35-10 



34-52 



36.48 

31.92 

50.97 

40.52 

27.50 

44-93 

34-65 



33-31 


. ... 

3i-52 

31-65 

55-98 

40.32 

25-45 

49-44 

34.15 



36.45 



41.49 

27-54 

56.69 

41.14 


... . 

33-50 

15-73 

50.75 

30.15 


28.63 



45.10 


. • v • 

36.36 

23.21 

45.08 

30.75 



34-42 



34-71 

27.46 


30.87 

19.66 

44.90 

28.42 

24.97 

43-03 

32.56 

• . • 


30.44 



36.55 

34-99 

















































































































54 


RAINFALL, 


Rainfall in the United States—( Continued ). 

GROUP 4 .—Upper Mississippi, part of Iowa, Minnesota, and 

Wisconsin. 


Station. 

Lat. 

Long. 

Height 

above 

Sea. 

Years 

of 

Record 

Min. 

Annual 

Rain. 

Max. 

Annual 

Rain. 

.Mean 

Annual 

Rain. 






Inches . 

Inches . 

Inches . 

Fort Ripley, Minn. 

46 °19' 

94 ° I 9 / 

1130 

17 

12.06 

36.14 

25.11 

Fort Snelling, “ . 

44 53 

93 10 

820 

22 

15-07 

49.69 

25.82 

Dubuque, Iowa. 

42 30 

90 40 

666 

15 

25.07 

47-19 

33-47 

Milwaukee, Wis. 

43 03 

87 55 

59 1 

23 

20.54 

44.86 

30.40 

Muscatine, Iowa. 

41 26 

9 i 05 

586 

19 

23.66 

74.20 

42.88 

Fort Madison, “ . 

40 37 

91 28 

600 

18 

27.54 

54- 1 4 

41.96 

33-27 


GROUP 5 .—Ohio River Valley, Western Pennsylvania to Eastern 

Missouri. 


Alleghany Arsenal, Penn 

Steubenville, Ohio. 

Marietta, “ . 

Cincinnati, “ . 

Portsmouth, “ . 

Athens, Ill. 

St. Louis Arsenal, Mo_ 

St. Louis, “ _ 

J efferson Barracks, “ ..., 


4 o° 32 ' 

8 o 0 O2' 

704 

23 

25.62 

47-79 

40 25 

80 41 

670 

37 

28.02 

57.28 

39 25 

81 29 

580 

48 

32.46 

53-54 

39 06 

84 25 

582 

3 1 

25-49 

65.18 

38 42 

82 53 

468 

26 

25.50 

56.79 

39 52 

89 5 6 

800 

16 

25.12 

48.17 

38 40 

90 10 

450 

19 

24.08 

71.54 

38 37 

90 16 

481 

28 

27.00 

68.83 

j 38 28 

9 ° U 

472 

21 

29.18 

55 -U 


35-23 

41.48 

42.70 

44.87 

38.33 

39.62 

42.63 
42.18 

40.88 


40.88 


GROUP 6.—Indian Territory and Western Arkansas. 


Fort Gibson, Ind. Ter.. 

Fort Smith, Ark. 

Fort Washita, Ind. Ter, 


35 ° 48 ' 

95°°3 

560 

20 

18.84 

55-82 

36.37 

35 23 

94 29 

460 

22 

24-34 

61.03 

40.36 

34 14 

96 38 

645 

16 

21.81 

64.29 

38.04 







38.25 


GROUP 7 .—Lower Mississippi and Red Rivers ; 


part of Kentucky. 


Springdale, Ken.. 
Washington, Ark 
Vicksburg, Miss. 
Natchez, “ . 


38°o 7 ' 

8 5 °2 4 ' 

57 o 

24 

30.91 

67.10 

48.58 

33 44 

93 4 i 

660 

22 

41.40 

70.40 

54-50 

32 23 

90 56 

350 

16 

37.21 

60.28 

49.30 

3 1 34 

9 1 25 

264 

18 

3!.09 

78.73 

53-55 







51.48 


GROUP 8.—Mississippi Delta, and Coast of Mississippi and Alabama. 


New Orleans, La. 

Mt. Vernon Arsenal, Ala. 

Baton Rouge, La. 


2 9 ° 57 / 

9O 0 O2' 

20 

23 

41.92 

67.12 

51.05 

3 1 12 

88 02 

200 

15 

51.49 

106.57 

66.14 

30 26 

OO 

M 

M 

O 

41 

15 

41.34 

116.40 

60.16 







59.12 


GROUP 9 .—Pacific 

San Francisco, Cal. 

Sacramento, “ . 

Fort Vancouver, W. Ter. 

Fort Steilacoom, “ . 

Sitka, Alaska. 


Coast, Bay of San 

Francisco to Alaska. 

37 ° 48 ' 

I22°26' 

170 

18 

n-73 

36.03 

21.69 

38 35 

121 28 

82 

18 

11.15 

27.44 

i 9-56 

45 40 

122 30 

50 

l6 

25.91 

56.09 

38.84 

47 IO 

122 25 

300 

16 

25.75 

70.21 

43-98 

57 03 

135 18 

20 

l6 

58.68 

95.8i 

83-39 







41.49 




























































































Fig. 3 



No. 1 . 

i . go 

1.80 
1.70 

1.60 

1.50 

1.40 

1.30 

1.20 

I.XO 

I 

.90 

.80 

.70 
.60 


No. 3. 


CURVES OF ANNUAL FLUCTUATIONS IN RAINFALL 


Atlantic sea-coast, Virginia to Florida. 
























































































































































































































































































































































































































































56 


RAINFALL. 


34. Monthly Fluctuations in Rainfall.— Our gener¬ 
alizations thus far have referred to the mean annual rainfall 
over large sections. There is a large range of fluctuation in 
the average amount of precipitation through the different 
seasons of the year, in different sections of the United 
States. It will be of interest to follow out this phase of the 
question in diagrams 3 and 4, in which type curves * of 
monthly means are drawn about a line of annual mean 

covering a series of years, in no case less than fifteen. 

* 

The letters J, F, M, &c., at the heads of the diagrams, 
are the initials of the months. The heavy horizontal lines 
represent means for the year, which are taken as unity. 
Their true values may be found at the foot of their respect¬ 
ive groups in the above table. About this line of annual 
mean is drawn by free-hand the type curve of mean rain¬ 
fall through the successive months, showing for each month 
its percentage of the annual mean. 

Each type curve relates to a section of country having 
uniform characteristics in its annual distribution of rain. 

Curve No. 1 , for Group No. 1, includes the section of 
country bordering upon the Atlantic sea-coast from Port¬ 
land to Washington. The average fluctuation of the year 
in this section is forty per cent. Its maximum rainfall 
occurs oftenest in August, and its minimum oftenest in 
January or February. 

Curve No. 2, for Group No. 2, includes the Atlantic 
coast border from Virginia to Florida. The average fluc¬ 
tuation of the year is one hundred and ninety-eight per 
cent. Its maximum rainfall occurs oftenest about the first 
of August, and nearly equal minima in April and October. 

* Reduced from a diagram by Clias. Schott, C. E., Smithsonian Contribu¬ 
tion, Vol. XVIII, p. 16 . The tables of American rainfall arranged by Mr. 
Schott, and published in the same volume, are exceedingly valuable. 





Miss. Delta, and coast of Miss. Ohio River Valley, Western 

and Alabama. Penn, to Eastern Missouri. 


Fig. 4. 


J F M A M J J A a 0 N D J 



1.50 ' 

1.40 

1.30 

1.20 

1.10 • 

1 

.90 

.80 

•7° . 
No. I 
1.30 ' 

1.20 

1.10 

1 

.90 

.80 

•70 . 


No. 7. 


CURVES OF ANNUAL FLUCTUATIONS IN RAINFALL, 


Indian Territory and Western ‘ Upper Miss., parts of Iowa, Minnesota, 

Arkansas. and Wisconsin. 










































































































































































































































































































































































































































































































































58 


RAINFALL. 


Curve No. 3, for Group No. 3, includes tlie upper Hud¬ 
son River valley, and northern and western New \ ork. 
The average fluctuation of the year is sixty-six per cent. 
Its maximum rainfall occurs oftenest near the first of July 
and its minimum oftenest about the first of February. 

Curve No. J, for Group No. 4, includes a part of Iowa, 
central Minnesota, and part of Wisconsin, in the upper 
Mississippi valley. The average fluctuation of the year is 
one hundred and nine per cent. Its maximum rainfall 
occurs oftenest in the latter part of June and its minimum 
oftenest about the first of February. 

Curve No. 5, for Group No. 5, includes the Ohio River 
valley, from western Pennsylvania to eastern Missouri. 
The average fluctuation of the year is seventy-three per 
cent. Its maximum rainfall occurs oftenest about the first 
of June and its minimum oftenest in the latter part of 
January. 

Curve No. 6 , for Group No. 6, includes the Indian Ter¬ 
ritory and Western Arkansas. The average fluctuation of 
the year is ninety-one per cent. Its maximum rainfall 
occurs oftenest about the first of May and its minimum 
oftenest at the opening of the year. 

Curve No. 8 , for Group No. 8, includes the Mississippi 
Delta and Gulf coast of Alabama and Mississippi. The 
average fluctuation of the year is seventy-five per cent. Its 
maximum rainfall occurs oftenest in the latter part of July 
and its minimum oftenest early in October. 

A similar type curve for Group No. 9, the region border¬ 
ing upon the Pacific coast from the Bay of San Francisco 
to Puget’s Sound, would show an average annual fluctua¬ 
tion through the seasons of two hundred and thirty-two 
per cent. The fluctuations here have nothing in common 
with the Mississippi and Atlantic types. The maximum 




Fig. 5. 



CURVES OF SECULAR FLUCTUATIONS IN RAINFALL. 
















































































































































































































































































60 


RAINFALL. 


rainfall here occurs oftenest in December and the minimum 
oftenest in July. 

35. Secular Fluctuations in Rainfall. —Diagram 5 
illustrates the secular fluctuations in the rainfall through a 
long series of years in the Atlantic system and in the central 
Mississippi system. It presents the successions of wet and 
dry periods as they vibrate back and forth about the mean 
of the whole period. 

The extreme fluctuation is in the first case twenty-eight 
per cent., and in the second case thirty per cent, 

36. Local, Physical, and Meteorological Influ¬ 
ences. —The above statistics give sufficient data for deter¬ 
mining approximately the general average rainfall in any 
one of the principal river-basins of the States. 

There are local influences operating in most of the main 
physical divisions, analogous to those governing rainfall in 
the grand atmospheric systems. 

Referring to any local watershed, and the detailed study 
of such is oftenest that of a limited gathering ground tribu¬ 
tary to some river, we have to note especially the mean 
temperature and capacity of the atmosphere to bear vapor, 
the source from which the chief saturation of the atmos¬ 
phere is derived, the prevailing winds at the different sea¬ 
sons, whether in harmony with or opposition to the direction 
of this source, and if any high lands that will act as con¬ 
densers of the moisture lie in its path and filch its vapors, 
or if guiding ridges converge the summer slioAvers in more 
than due proportion in a favored valley. A careful study 
of the local, physical, and meteorological influences will 
usually indicate quite unmistakably if the mean rainfall of 
a subordinate watershed is greater or less than that of the 
main basin to which its streams are tributary. There is 
rarely a sudden change of mean precipitation, except at the 


GREAT RAIN STORMS. 


61 


crest of an elevated ridge or tlie brink of a deep and narrow 
ravine. 

37. Uniform Effects of Natural Laws. — When 
studies of local rainfalls are confined to mean results, 
neglecting the occasional wide departures from the influence 
of the general controlling atmospheric laws, the actions of 
nature seem precise and regular in their successions, and in 
fact we find that the governing forces hold results with a 
firm bearing close upon their appointed line. 

But occasionally they break out from their accustomed 
course as with a convulsive leap, and a storm rages as 
though the windows of heaven had burst, and floods sweep 
down the water-courses, almost irresistible in their fury. 
If hydraulic constructions are not built as firm as the ever¬ 
lasting hills, their ruins will on such occasions be borne 
along on the flood toward the ocean. 

38. Great Rain Storms. —In October, 1869, a great 
storm moved up along the Atlantic coast from Virginia to 
New York, and passed through the heart of New England, 
with disastrous effect along nearly its whole course. Its 
rainfall at many points along its central path was from 
eight to nine inches, and its duration in New England was 
from forty to fifty-nine hours. 

In August, 1874, a short, heavy storm passed over east¬ 
ern Connecticut, when there fell at New London and at 
Norwich twelve inches* of rain within forty-eight hours, 
five inches of which fell in four hours. Such storms are 
rare upon the Atlantic coast and in the Middle and West¬ 
ern States. 

Short storms of equal force, lasting one or two hours, 
are more common, and the flood effects from them, on hilly 


* From data supplied by II. B. Winsliip, Supt. of Norwich Water-works. 




62 


RAINFALL. 


watersheds, not exceeding one or two square miles area, 
may be equally disastrous, and waterspouts sometimes 
burst in the valleys and hood their streams. 

39. Maximum Ratios of Floods to Rainfalls.— 
When the surface of a small watershed is generally rocky, 
or impervious, or, for instance, when the ground is frozen 
and uncovered by snow, the maximum rate of volume of 
how through the outlet channel may reach two-thirds of the 
average rate of volume of rain falling upon the gathering- 
ground. 

40. Volume of Water from given Rainfalls.—The 

rates of volume of water falling per minute, for the rates of 
rainfall per twenty-four hours, indicated, are given in cubic 
feet per minute, per acre and per square mile, in the follow¬ 
ing table: 


TABLE No. 8. 

Volume of Rainfall per Minute, for given Inches per Twenty- 

four Hours. 


Rainfall per 
24 HOURS. 

Volume per 
Minute on 
. One Acre. 

Volume per 
Minute on 
One Sq. Mile. 

Inches. 

Cu. feet. 

Cu. feet. 

0.1 

.252 

161.33 

.2 

• 5°4 

322.67 

•3 

• 75 6 

484.OI 

‘4 

1.008 

645-33 

•5 

I.264 

806.67 

.6 

I -S I 5 

968.OO 

•7 

!- 7 6 5 

II22.73 

.8 

2.107 

1290.67 

•9 

2.269 

I450.OO 


Rainfall 

per 

24 HOURS. 

Volume per 
Minute on 
One Acre. 

Volume per 
Minute on 
One Sq. Mile„ 

Inches. 

Cu. feet. 

Cu. feet. 

I 

2 . 5 21 

1613.31: 

2 

5.042 

3226.62 

3 

7-563 

4840.00- 

4 

IO.084 

6453-25 

5 

12.605 

8066.56 

6 

15.126 

9679.87 

7 

l7- 6 47 

11293.18 

8 

20.168 

12906.50 

9 

22.689 

i 45 2 9-8 1 

10 

25.200 

16133.12 


41. Gauging Rainfall.— A pluviometer, Fig. 6, is used 
to measure the amount of rain that falls from the sky. It is 
a deep, cylindrical, open-topped disli of 1>rass. Its top 





















GAUGING RAINFALL. 


63 


edge is thin, so it will receive just tlie rain due to the sec¬ 
tional area of tlie open top. » 

A convenient size is of two inches diameter at a, and at 
b of such diameter that its sectional 
area is exactly one-tenth the sec¬ 
tional area at a, or a little more 
than one-half inch. 

When extreme accuracy is re¬ 
quired, the diameter at a is made 
ten inches and at b a little more 
than three inches, still maintaining 
the ratio of sectional areas ten to 
one , the displacement of the meas¬ 
uring-rod being allowed for. 

This rain-gauge should be set 
vertically in a smooth, open, level 
ground, and the grass around be 
kept smoothly trimmed in summer. 

The top of a ten-inch gauge is set 
at about one foot above the surface 
of the ground, and of smaller 
gauges, clear of the grass surface. 

The gauge should be placed sufficiently apart from 
buildings, fences, trees, and shrubs, so that the volume of 
rain gathered shall not be augmented or reduced by wind- 
eddies. 

If such a situation, secure from interference by animals 
or by mischievous persons, is not obtainable, the gauge 
may be set upon the flat roof of a building, and the height 
above the ground noted. 

The measuring-rod for taking the depth of rain in b is 
graduated in inches and tenths of inches, so that when the 
sections of a and b are ten to one , ten inches upon the rod 





































64 


RAINFALL. 


corresponds with one inch of actual rainfall, and one inch 
on the rod to one-tenth inch of rain, and one-tenth on the 
rod to one-liundredth of rain. 

Snow is caught in a cylindrical, vertical-sided dish, not 
less than ten inches diameter, melted, and then measured as 
rain. Memorandums of depths of snow before melting, 
with dates, are preserved also. 

It has been observed at numerous places, that elevated 
pluviometers indicated less rain than those placed in the 
neighboring ground. When there is wind during a shower, 
the path of the drops is parabolic, being much inclined in 
the air above and nearly vertical at the surface of the 
ground. A circular rain-gauge, held horizontally, presents 
to inclined drops an elliptic section, and consequently less 
effective area than to vertical drops. 

The law due to height alone is not satisfactorily estab¬ 
lished, though several formulae of correction have been 
suggested, some of which were very evidently based upon 
erroneous measures of rainfall. 

The observed rainfall at Greenwich Observatory, Eng¬ 
land, in the year 1855, is reported, at ground level, 23.8 
inches depth; at 22 feet higher, .807 of that quantity, and 
at 50 feet higher, .42 of that quantity. 

The observed rainfall at the Yorkshire Museum, Eng¬ 
land, in the years 1832, 1833, and 1834, is reported, for 
yearly average, at ground level, 21.477 inches; at 44 feet 
higher, .81 as much, and at 213 feet higher, .605 as much. 

Unless vigilantly watched during storms, the gauges are 
liable to overflow, when an accurate record becomes impos¬ 
sible. Overflow cups are sometimes joined to rain-gauges, 
near their tops, to catch the surplus water of great storms. 












































































































































































. 




































































































■ 






■ > r 













































































































Fig. 127. Fig. 128. 









SECTION AND PLAN OF PUMP HOUSE. 







































































































































































CHAPTER IV. 


FLOW OF STREAMS. 

42. Flood Volume Inversely as the Area of the 
Basin.— A rain, falling at the rate of one inch in twenty- 
four hours, delivers upon each acre of drainage area about 
2.5 cubic feet of water each minute. 

If upon one square mile area, with frozen or impervious 
surface, there falls twelve inches of rain in twenty-four 
hours, and two-thirds of this amount flows off in an equal 
length of time, then the average rate of flow will be 215 
cubic feet per second. 

Any artificial channel cut for a stream, or any dam 
built across it, must have ample flood-way, overfall, or 
waste-sluice to pass the flood at its maximum rate. 

The rate of flood flow at the outlet of a watershed is 
usually much less from a large main basin than from its 
tributary basins, because the proportion of plains, storage 
ponds, and pervious soils is usually greater in large basins 
than in small, and the flood flow is consequently distrib¬ 
uted through a longer time. 

In a small tributary shed of steep slope the period of 
maximum flood flow may follow close after the maximum 
rainfall; but in the main channel of the main basin the 
maximum flood effect may not follow for one, two, three, or 
more days, or until the storm upon its upper valley has 
entirely ceased. 

43. Formulae for Flood Volumes.— The recorded flood 
measurements of American streams are few in number, but 

5 



66 


FLOW OF STREAMS. 


upon plotting such data as is obtained, we find their mean 
curve to follow very closely that of the equation, 

Q = 200 (M)*, (1) 

in which M is the area of watershed in square miles and Q 
the volume of discharge, in cubic feet per second, from the 
whole area. 

Thus the decrease of flood with increase of area is seen 
to follow nearly the ratio of two hundred times the sixth 
root of the fifth power of the area expressed in square 
miles. 

Among the Indian Professional Papers we find the fol¬ 
lowing formula for volume, in cubic feet per second : 

Q = x 27 (M) K (2) 

in which c is a co-efficient, to which Colonel Dickens has 
given a mean value of 8.25 for East Indian practice. 

Testing this formula by our American curve, we find the 
following values of c for given areas : 


Area in sq. miles... 

I. 

2. 

3 - 

4 - 

6. 

8. 

10. 

i 5 - 

20. 30. 

40. 

5 °- 

75 - 

IOO. 

Value of c . 

7 - 4 1 

9-33 

10.68 

11.76 

13.46 

14-83 

15.96 

18.26 

20.11 23.02 

25-33 

27.28 

31.26 

34-38 


Mr. Dredge suggests, also in Indian Professional Papers, 
the following formula : 

M 

Q = 1300 x , (3) 

in which L is the length of the watershed, and M the area 
in square miles. 

Our formula, modified as follows, gives an approximate 
flood volume per square mile, in cubic feet per second: 



200 (My 

M 


( 4 ) 




















TABLE OF FLOOD VOLUMES. 


67 


in which M is the area of the given watershed in square 
miles. 

44. Table of Flood Volumes. —Upon the average 

New England and Middle State basins, maximum floods 
may be anticipated with rates of flow, as per the following 
table: 

TABLE No. 9. 

Flood Volumes from given Watersheds. 


Flood Discharge 
for Whole Area, 

Q = 200 (M)' 1 ' 


Flood Discharge per 
Square Mile, 

200 (M)®’ 


Q = 


M. 


Area of Water¬ 
shed. 


Sq. Miles. 

o-5 

1 

2 

3 

4 
6 
8 

io 

i5 

20 

25 

30 

40 

5 ° 

75 

100 

200 

3 °° 

400 

5 °° 

600 

800 

1000 

15°° 

2000 

3000 

4000 

5 °°° 


Cu. Feet per Second. 

112 
200 
356 
5 °° 

6 35 

890 

1131 

1362 

1910 

2428 

2924 

34°4 

4326 

52 10 

73°4 

9283 

16542 

23190 

29480 

355 °° 

4 i 3 2 ° 

5 2 5 2 ° 
63242 
88680 
112700 
158000 
200900 
241800 


Cu. Feet per Second. 

225.OO 

200.00 

178.20 

166.53 

158.75 

148.37 

141.42 

136.26 

127.33 

12 I.40 
117.OO 

H 3-47 

108.15 

104.16 

97-39 

92.83 

82.71 

77-3o 

73-7o 

71.00 

68.87 

65-65 

63.26 

59- 12 

56.35 
52.67 
50.20 

48.36 


Flood Discharge 
per Acre. 


Cu. Feet per Minute. 

21.10 

18.75 

16.75 
I5-65 

14.86 

I 3-9 I 

13.26 

12.48 

11.94 

11.38 

11.97 

10.64 

10.14 

9-77 

9- I 5 

8.72 

7-77 

7.26 

6.93 
6.67 
6.46 
6.16 

5-94 

5-55 

5- 2 * 4 5 9 

4.94 

4.72 
4-54 


















68 


FLOW OF STREAMS. 


45. Seasons of Floods. — Great floods occur only 
when peculiar combinations of circumstances favor such 
result. 

A knowledge of the magnitude of the floods upon any 
river, and of their usual season, is invaluable to the director 
of constructions upon that stream, to enable him to take such 
precautionary measures as to be always prepared for them. 
Such knowledge is also requisite to enable him to compute 
the storage capacity required to save and utilize such flood, 
or to calculate the sectional area of waste weir required 
upon dams to safely pass the same. 

Long rivers, having their sources upon northern moun¬ 
tain slopes, have usually well-known seasons of flood, de¬ 
pendent upon the melting of snows ; but small watersheds 
in many sections of America are subject to flood, alike, at 
all seasons. 

40. Influence of Absorption and Evaporation 
upon Flow. —The rainfall upon the Atlantic coast and 
upon the Mississippi valley appears comparatively uniform 
when noted in its monthly classification, but the ability of 
any one of their watersheds to supply, from flow of stream, 
a domestic demand equal to its mean flow is by no means 
as uniform. 

We have seen that, according to the statistics quoted, 
the consumption of water is not as uniform, when noted by 
monthly classification, as is the monthly rainfall. When 
lesser classifications of rainfall and consumption are com¬ 
pared, there is scarce a trace of identity in their plotted 
irregular profiles. 

Evaporation, though comparatively uniform in its 
monthly classification, is very irregular as observed in its 
lesser periods. 

In the spring and early summer, when vegetation is in 



CLASSIFICATION OF RAINFALL AVAILABLE IN FLOW. 69 


most thrifty growth, the innumerable rootlets of flowers, 
grasses, shrubs, and forests, gather in a large proportion of 
rainfall, and pass it through their arteries and back into 
the atmosphere beyond reach for animal uses. 

47. Flow in Seasons of Minimum Rainfall. —In 
gathering, basins having limited pondage or available 
storage of rainfall, the flow from minimum annual, and 
minimum periodic rainfall demands especial study. Occa¬ 
sionally the annual rainfall continues less than the general 
mean through cycles of three or four years, as is indicated 
in tbe above diagram of curves of secular rainfall. The 
mean rain of such cycles of low-rainfall is occasionally less 
than eight-tenths of the general mean. 

We have selected for data upon this point the rainfall 
records of twenty-one stations, of longest observation in the 
United States, at various points from Maine to Louisiana 
and from California to Sitka. The computation gives the 
annual rainfall of the least three-year cycle at any one of 
these points as .67 of the general mean annual rain at the 
same point, and annual rainfall of the greatest three-year 
low cycle as .97 of the general mean at the same point. An 
average of all these stations gives the three-year low cycle 
rainfall as .81 of the average mean annual rainfall. 

48. Periodic Classification of Rainfall Available 
in Flow. —Next, the rainfall and the portion of it that can 
be made available, demands especial study in its monthly, 
or less periodic classification. It is desirable to know the 
ratio of each month’s average fall to the mean monthly fall 
for the year, and,the percentage of this fall that is exempted 
from absorptions by vegetation and evaporations into the 
atmosphere, and that flows from springs, and in the streams, 
since it is ordained by Nature that the lily and the oak 
with their seed, shall first be supplied and the atmospheric 


70 


FLOW OF STREAMS. 


processes be maintained, and the surplus rain be dedicated 
to the animal creation, as their necessities demand and 
ingenuities permit them to make available. 

49. Sub-surface Equalizers of Flow. —The inter¬ 
stices of the soils and the crevices of the rocks were filled 
long ages ago, and now regularly aid in equalizing the flow 
of the springs and streams without, to any considerable 
extent, affecting the total annual flow, yet their influence is 
observable in cycles of droughts when the sub-surface water 
level is drawn slowly down. 

The substructure of each given watershed has its indi¬ 
vidual storage peculiarities which may increase or diminish 
the monthly flow and degree of regularity of flow of its 
streams to an important extent. 

If a porous subsoil of great depth and storage capacity 
is overlaid with a thin crust of soil through which water 
percolates slowly, a great flood-rain may fall suddenly over 
the nearly exhausted sub-reservoir and be run off to the 
rivers without replenishing appreciably the waning springs, 
or increasing their flow as would an ordinary slow rainfall. 

On the other hand, if its surface soil is open and absorb¬ 
ent, it may be able to receive nearly the whole flood and 
distribute it gradually from its springs. 

The early sealing over of the subsoil by winter frosts 
before the usual subterranean storage has accumulated 
from winter storms, or a shedding of the melting snows in 
spring by a like frost-crust, may result in a diminished flow 
of the deep springs in the following summer. 

Subsoils that exhaust themselves in ordinary seasons 
are comparatively valueless to sustain the flow in the second 
and third years of cycle droughts. 

Steep and impervious earths yield no springs, but gather 
their waters rapidly in the draining streams. 


SUMMARIES OF MONTHLY FLOW STATISTICS. 


71 


50. Flashy and Steady Streams.— Upon tlie steep 
and rocky watersheds of northern New Hampshire, we find 
extreme examples of “ flashy” streams that are furious in 
storm and vanish in droughts. 

Upon the saturated sands of Hempstead Plains on Long 
Island, 1ST. Y., we find an opposite extreme of constant and 
even flow, where a great underground reservoir co-extensive 
with its supplying watershed, feeds its streams with remark¬ 
able uniformity. 

Almost all degrees of constancy and fickleness of flow 
are to be found in the several sub-section streams of any 
one of our great river basins. 

51. Peculiar Watersheds. —The extremes or results 
from peculiar watersheds, are in all cases to be considered 
as extremes when their individual merits and capacities of 
supply are investigated, and the investigation may often 
take the direction of determining the relations of its results 
to results from a general mean, or ordinary watershed, 
especially as respects its mean temperature, its mean hu¬ 
midity of atmosphere, the direction from whence its storms 
come, the frequency of its storm winds, the extent of its 
storms in the different seasons, the imperviousness or the 
porosity of its soils and rocks, the proportions of its steep, 
gently undulating, and flat surfaces, and also it is to be 
observed if it can be classed among those rare instances in 
which one watershed is tributary as giver to or receiver 
from another basin, involving an investigation of its geo¬ 
logical substructure. 

52. Summaries of Monthly Flow Statistics.— 

We have analyzed some valuable statistics of monthly 
rainfalls, and measured flow of streams in Massachusetts 
and New York State, which are too voluminous for repro¬ 
duction here, and present the deduced results. The records 


72 


FLOW OF STREAMS. 


are, first, from a report by Jos. P. Davis, C. E., relating to 
the watershed of Cochituate Lake, which has supplied the 
city of Boston with water until supplemented in 1876 from 
the Sudbury River watershed; second, from a table com¬ 
piled by Jas. P. Kirkwood, C. E., relating to the watershed 
of Croton River above the Croton Dam ; and third, from a 
paper read by J. J. R. Croes, C. E., before the American 
Society of Civil Engineers, July, 1874, relating to the water¬ 
shed of the West Branch of the Croton River. 

Additional statistics relating to Sudbury River are given 
on page 83a. 

The summaries are as follows: 


TAB LE No. 1 O. 

Summary of Rainfall upon the Cochituate Basin. 

Average annual, 55.032 inches ; average monthly, 4.586 inches. 



5 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

fci 

D 

< 

Sept. 

Oct. 

Nov. 

Dec. 

Mean.. 

Minimum. 

Maximum. 

Ratio of monthly 
mean. 

in. 

3-69 

I -3 I 

7-85 

in. 

403 

.98 

5.80 

in. 

5-35 

2.51 

8.44 

in. 

4-58 

1.94 

”•34 

in. 

5-69 

2.66 

8.25 

in. 

3-09 

.58 

5-96 

in. 

5-23 

1.06 

14.12 

in. 

4.91 

2.03 

12.36 

in. 

3 - 8 i 

.64 

8.49 

in. 

5-86 

1.19 

9-5° 

in. 

5.26 

2.63 

8-54 

in. 

3-52 

•45 

5-98 

.806 

.878 

1.167 

.998 

I.241 

•675 

I,I4I 

1.070 

.831 

1.300 

r.i47 

.768 


TABLE No. 1 1. 

Summary of Rainfall upon the Croton Basin. 


Average annual, 46.497 inches ; average monthly, 4.227 inches. 



Jan. 

Feb. 

1 

Mar. 

Apr. 

May. 

June. 

July. 

bi 

3 

< 

Sept. 

Oct. 

Nov. 

Dec. 

Mean. 

Minimum. . 

Maximum. 

Ratio of monthly 
mean. 

in. 

2-54 

.96 

4.18 

in. 

3 -i 5 

I * 1 5 

5-03 

in. 

3.16 

1.89 

5-64 

in. 

3.12 

2.48 

4 - 3 2 

in. 

6.40 

4.78 

TO. l8 

in. 

4-58 

2.51 

6.19 

in. 

4 - 3 i 

2.31 

8.12 

in. 

6.03 

2.30 

9.21 

in. 

5-30 

2.23 

13-35 

in. 

4.70 

•74 

8.74 

in. 

3-83 

3-09 

5-36 

in. 

3.60 

1.86 

6.86 

.625 

•745 

•749 

•739 

I- 5 I 3 

1.084 

X.020 

1.427 

1.259 

1.hi 

• 9°5 

.851 




























































































SUMMARIES OF MONTHLY FLOW STATISTICS. 


73 


TABLE No. 12. 

Summary of Rainfall upon Croton West-Branch Basin. 


Average annual, 44.429 inches ; average monthly, 4.039 inches. 



d 

d 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

1 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean. 

Minimum. 

Maximum. 

Ratio of monthly 
mean. 

in. 

3.16 

1.44 

4 - 5 i 

in , 
3.20 
1.22 
6.40 

in. 

3-30 

2-55 

4.27 

in . 

3-84 

3 - QI 

5-45 

in. 

5 -oS 

2.30 

8.79 

in. 

4 - 32 
2.06 

5 - 73 

in. 

4-59 

3-43 

5.52 

in . 

6.59 

5.10 

10.04 

in. 

2.90 

1.44 

3- 6 9 

in. 

5-24 

2-15 

9.46 

in. 

3.10 

243 

4-35 

in. 

3.16 

1.49 

5-96 

•783 

.767 

1.296 

.718 

1-633 

1.136 

I.O7O 

1-257 

• 95 i 

.818 

•793 

.783 


TABLE No. 13. 

Summary of Percentage of Rainfall Flowing from the Cochit- 

uate Basin. 


Average percentage of average annual rainfall flowing off, 45.6. 



Jan. 

Feb. 

Mar. 

Apr. 

£ 

ci 

§ 

June. 

W 

*—< 

*—> 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 


in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

Mean. 

52.5 

79-7 

7 x -3 

80.5 

45- 1 

35-i 

20.3 

20.0 

24-5 

26.5 

27.8 

64-3 

Minimum. 

33 

26 

44 

39 

20 

9 

9 

14 

!3 

IO 

20 

24 

Maximum. 

79 

159 

I 53 

124 

76 

84 

39 

27 

39 

80 

42 

261 

Ratio of monthly 










.58 

.61 


mean. 

1.15 

i-75 

1.56 

1.77 

•97 

.770 

•44 

■44 

•54 

1.41 


TABLE No. 14. 

Summary of Percentage of Rainfall Flowing from the Croton 

Basin. 

Average percentage of average annual rainfall flowing off, 57.47. 



d 

d 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

1 

bio 

P 

< 

Sept. 

Oct. 

Nov. 

Dec. 

Mean. 

in. 

79.68 

49.0 

123.4 

in. 

75 -o 

62.1 

107.0 

in. 

86.72 

21.9 

147.4 

in. 

80.60 

53-5 

125.7 

in. 

48-45 

42.8 

56.4 

in. 

45.02 

18.6 

67.4 

in. 

21.02 

8-5 

29.6 

in. 

19-45 

8.4 

42.2 

in. 

30.10 

10.2 

92.0 

in. 

81.13 

7.6 

366.5 

in. 

60.40 

36-3 

94.1 

in. 

62.12 

39 -o 

94-5 

Minimum. 

Maximum. 

Ratio of monthly 
mean. 

1.386 

i- 3°5 

1.509 

1.402 

•843 

.783 

•369 

•338 

•524 

1.412 

1.051 

1.081 
































































































































74 


FLOW OF STREAMS. 


TABLE No. 15. 

Summary of Percentage of Rainfall Flowing from the Croton 

West-Branch Basin. 


Average percentage of average annual rainfall flowing off, 70.98. 



Jan. 

Feb. 

Mar. 

c. 

<5 

May. 

June. 

July. 

Aug. 

Sept. 

Oct 

Nov. 

Dec. 

Mean, . 

in. 

102.8 

17.7 

186.6 

in. 
71.1 
59 -o 
io 3-9 

in. 

158.9 

103.0 

209.1 

in. 

117.2 

93-2 

158-4 

in. 

80.5 

46.7 

100.3 

in. 

44.8 

I7.6 

71.2 

in. 

19.0 

7-3 

3 i -4 

in. 

24.6 

3-4 

53-8 

in. 

26.6 

3-3 

39-8 

in. 

3°-4 
11.2 

56-3 

in. 

78.9 

40.5 

110.2 

in. 

97.0 

65.6 

140.8 

Minimum.... 

Maximum. „. 

Ratio of monthly 
mean.. 

1.448 

I.OOI 

2.238 

1.651 

i-i 34 

.636 

.267 

•347 

•375 

.428 

I.II2 

1.367 



TABLE No. 16. 


Summary of Volume of Flow of Rainfall from the Cochituate 
Basin (in cubic feet per minute per square mile). 



d 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

O 

O 

Nov. 

Dec. 

Mean. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

cu.ft. 

99.17 

150.42 

174.76 

169.80 

131.80 

44.27 

45-27 

49-15 

42.84 

62.45 

75 - 9 ° 

78.94 

Minimum. 

37-99 

58.29 

91.60 

7°-44 

67.14 

18.28 

21.34 

2 i -34 

4 - 3 o 

36.43 

47-32 

40.07 

Maximum...... 

245.12 

301.90 

242.52 

369.40 

321.11 

85-49 

154-57 

IO9.29 

99.48 

123.34 

105-39 

164. g& 

Ratio of monthly 
mean. 

1.058 

1.605 

1.865 

1.812 

1.406 

.472 

•483 

•524 

•457 

.666 

.809 

.842 


TABLE No. 17. 


Summary of Volume of Flow of Rainfall from the Croton 
Basin (in cubic feet per minute per square mile). 



d 
►“—» 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean. 

Minimum. 

Maximum. 

Ratio of monthly 
mean. 

cu.ft. 

91.48 

48.08 

127.71 

cu.ft. 

147.69 

40.65 

293.01 

cu.ft. 

177.02 

79-°5 

25.709 

cu.ft. 

132.63 

87-43 

188.95 

cu.ft. 

164.49 

108.25 

298.98 

cu.ft. 

115.12 

34-09 

224-33 

cu ft. 

48-37 

10.46 

81.76 

cu.ft . 
70.22 

I 3 * 12 

202.19 

cu.ft. 

85-99 

12.91 

275-95 

cu.ft. 

81.08 

18.05 

141.14 

cu.ft. 

124.92 

61.41 

201.30 

cu ft. 

106.23 
72.08 

146.24 

.816 

i- 3 i 7 

*•579 

1.183 

1.467 

1.027 

•431 

.627 

.767 

•723 

1.114 

.948: 































































































































SECTIONS OF CROTON NEW AQUEDUCT, 1886. 






mem **&■ 






















































































MINIMUM, MEAN, AND FLOOD FLOW OF STREAMS. 75 


TABLE No. 18. 


Summary of Volume of Flow of Rainfall from the Croton 
West-Branch Basin (in cubic feet per minute per square mile). 



Jan. 

A 

<u 

fa 

Mar. 

1 Apr. 

1 


| June. 

3 

1—i 

bi 

P 

<5 

a 

<D 

c n 

0 

O 

> 

0 

£ 

Dec. 


cu . ft . 

CU./t- 

cuft . 

cu . ft . 

cu . ft . 

cu . ft . 

cu . ft . 

cu . ft . 

cu . ft . 

cuft . 

cu . ft . 

cu . ft . 

Mean. 

158.95 

185.19 

290.56 

272.60 

161.60 

104.86 

40.02 

103.12 

r 47-59 

96.26 

107.85 

164.07 

Minimum.. 

35-o8 

47.16 

203.58 

146.04 

26.19 

45 - 1 8 

19.26 

9.06 

5.16 

27.48 

5-92 

50.88 

Maximum. 

347.88 

378.90 

390-83 

463.98 

394.92 

202.02 

85.56 

281.04 

477.22 

277.26 

203.28 

299.16 

Ratio of monthly 
mean.. 

I.O4I 

1.213 

1.904 

1.786 

1.059 

.680 

.262 

.676 

.967 

.631 

.707 

I>0 75 


53. Minimum, Mean, and Flood Flow of Streams. 

—An analysis of the published records of volumes of water 
flowing in the streams in all the seasons has led to the fol¬ 
lowing approximate estimate of volumes of flow in the aver¬ 
age Atlantic coast basins: 

The minimum refers to a fifteen days’ period of least 
summer flow. 

The mean refers to a one hundred and twenty days’ 
period, covering usually July, August, September, and 
October, beginning sometimes earlier, in June, and ending 
sometimes later, in November. 

The maximum refers to flood volumes. 


TABLE No. 19. 

Estimates of Minimum, Mean, and Maximum Flow of Streams. 



Min. in cu. ft. per 
sec. per sq. mi. 

Mean in cu. ft. per 
sec. per sq. mi. 

Max. in cu ft. per 
sec. per sq. mi. 

Area of watershed, 1 

sq. mi. 

.083 

1.00 

200 

a 

u 

a 

IO 

a 

.1 

•99 

136 

a 

a 

a 

2 5 

a 

.11 

.98 

n 7 

it 

a 

a 

5 ° 

a 

.14 

•97 

104 

a 

a 

a 

100 

a 

.18 

•95 

93 

it 

a 

tt 

250 

a 

• 2 5 

.90 

80 

it 

a 

it 

coo 

a 

• 3 ° 

.87 

7 1 

it 

it 

a 

1000 

a 

•35 

.82 

6 3 

tt 

a 

it 

1500 

a 

•38 

.80 

59 

a 

it 

it 

2000 

u 

.41 

•79 

56 























































76 


FLOW OF STREAMS. 


This table refers to streams of average natural pondage 
and retentiveness of soil, but excludes effects of artificial 
storage. The fluctuations of streams will be greater than 
indicated by the table when prevailing slopes are steep and 
rocks impervious, and less in rolling country with pervious 
soils. 

54. Ratios of Monthly Flow in Streams. —A care¬ 
ful analysis of the published records of monthly How of the 
average Atlantic coast streams leads to the following ap¬ 
proximate estimate of the ratio of the monthly mean rain¬ 
fall that flows down the streams in each given month of the 
year, in which due consideration of the evaporation from 
soils and foliage in very dry seasons has not been neglected. 


TABLE No. 2 0. 
Monthly Ratios of Flow of Streams. 



Jan. 

x 3 

<u 

March. 

April. 

May. 

1 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Ratio of flow . 

1.65 

1.50 

1.65 

i -45 

.85 

•75 

•35 

•25 

•30 

•45 

1.20 

1.60 


Here unity equals the mean monthly flow, or one-twelfth 
the mean annual flow. 

To compute, approximately, the inches depth of rain 
flowing in the streams each month, one-twelfth the mean 
annual rain, at the given locality, may be multiplied by the 
ratios in the following table. For illustration, a mean 
annual rain of 40 inches depth, giving 3.333 inches mean 
monthly depth, is assumed, and the available flow of stream 
expressed in inches depth of rain is added after the ratios. 





























MEAN ANNUAL FLOW OF STREAMS. 


77 


TABLE No. 21 . 


Ratios of Mean Monthly Rain, and Inches of Rain Flowing 

each Month. 



d 

0$ 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

+3 

0 

0 

> 

0 

Dec. 

Ratios of mean 
monthly rain 

.825 

• 75 ° 

.825 

•725 

•425 

•375 

•i 75 

.125 

.150 

.225 

.600 

.800 

Inches of rain 










flowing. 

2-75 

2.50 

2.75 

2.41 

1.41 

1.25 

o -59 

0.41 

0.50 

0.75 

2.00 

2.66 

Eight - tenths 




of same. 

2.20 

2.00 

2.20 

i -93 

M 

H 

u> 

1.00 

0.47 

o -33 

0.40 

0.60 

1.60 

2.13 


For low-cycle years, use eiglit-tentlis (§ 47) tlie available 
monthly depth of rain flowing. 

55. Mean Annual Flow of Streams. —When month¬ 
ly data of the flow of any given stream is not obtainable, it 
may ordinarily be taken upon average drainage areas, for 
an annual flow, as equal to fifty per cent, of the annual 
rainfall. 

Or, for different surfaces, its ratio of the annual rain, 
including floods and flow of springs, is more approximately 
as follows: 

From mountain slopes, or steep rocky hills.8o to .90 


Wooded, swampy lands.60 to .80 

Undulating pasture and woodland.50 to .70 

Flat cultivated lands and prairie.45 to .60 


Since stations for meteorological observations are now 
established in or near almost all the populous neighbor¬ 
hoods, and some of the stations have already been estab¬ 
lished more than a quarter of a century, it is easier to obtain 
data relating to rainfall than to the flow of streams. In 
fact, the required data relating to a given stream is rarely 
obtainable, and the estimates relating to the capacity and 




































78 


FLOW OF STREAMS. 


reliability of the stream to furnish a given water-supply 
must necessarily be quite speculative. 

56. Estimates of Flow of Streams.—In such case, 
an estimate of the capacity of a stream to deliver into a 
reservoir, conduit, or pump-well is computed according to 
some scheme suggested by extended observations and study 
of streams and their watersheds, and long experience in the 
construction of water supplies. 

The first reconnoissance of a given watershed by an ex¬ 
pert in hydrology will ordinarily enable him to judge very 
closely of its capacity to yield an available and suitable 
water supply; for his comprehension at once grasps its 
geological structure, its physical features and its usual 
meteorological phenomena, and his educated judgment 
supplies the necessary data, as it were, instinctively. 

If the estimate of flow of a stream must be worked up 
from a survey of the watershed area and the mean annual 
rainfall, as the principal data, then recourse may be had to 
the data and estimates given above, relating to the question, 
for average upland basins of one hundred or less square 
miles area. 

In illustration, let us assume a basin of one square mile 
area, having a forty-inch average annual rainfall, and then 
proceed with a computation. This is a convenient unit of 
area upon which to base computations for larger areas. 

The ratios of the three-year low rain cycles gives their 
mean rainfall as about eight-tenths of the general mean 
rainfall. We assume it to be eighty per cent. The mean 
annual flow of the stream we assume to be fifty per cent, of 
the annual rainfall. Eight-tenths of fifty per cent, gives 
forty per cent, of the annual rainfall as the annual available 
flow of the stream, and forty per cent, of the forty inches 
rainfall gives an equivalent of sixteen inches of rainfall 


ESTIMATES OF FLOW OF STREAMS. 


79 


flowing down the stream annually. The monthly average 
flow is then taken as one-twelfth of sixteen, or one and one- 
third inches. Our estimated monthly percentage of mean 
flow, as given above (§ 54), is sometimes much in excess 
and sometimes less than the monthly average. Flows less 
than the mean are to be compensated for by a proportion¬ 
ate increase of storage above the mean storage required. 

The monthly computations are as follows: 


Monthly mean = 


40 inches x 50 per cent, x .8 


lo+i — 1.833 

12 months 

inches average available rain monthly. This average mul¬ 
tiplied by the respective ratios of flow in each month gives 
the inches depth of available rain flowing in the respective 
months, thus: 


January . 

Mean Monthly 
Rainfall. 

X 

Respective 

Ratios. 

I.65 


Inches Depth of 
Available Rain 
Flowing each 
Month. 

2.20 

February — 

U 

X 

I.50 

~~~~ 

2.00 

March . 

n 

X 

I.65 


2.20 

April . 

ii 

X 

1-45 

— 

1-93 

May . 

u 

X 

•85 


1 .13 

June. 

a 

X 

•75 

1 1 

I.OO 

July. 

a 

X 

•35 


47 

August . 

n 

X 

•25 

= 

•33 

September. . 

a 

X 

•30 

— 

.40 

October .... 

<< 

X 

45 

= 

.60 

November. . 

(C 

X 

1.20 

— 

1.60 

December .. 

a 

X 

1.60 

— 

2.14 




we have 

.8 

x .50 

Again, uniting the constants, 

V 2 — = .033; 


which, multiplied by the respective ratios of monthly flow, 
thus: Jan., .0333 x 1.65 = .055, etc., gives directly the mean 
ratio of the low cycle annual rainfall that is available in the 
stream each month. 


















80 


FLOW OF STREAMS. 









Flow in Cu. Ft. per 








Minute per Sq. Mi. 








in 

each Month. 

jan.. 


X 

•055 

= 

2.20 

inches depth = 

116.60 

Feb.. 

X 

.050 


2.00 


= 

106.00 

March... 

X 

.055 


2.20 


zzz 

116.60 

April 

• • • 

X 

.0483 

= 

i -93 


= 

102.29 

May.. 


X 

.0283 

— 

113 

u 


59-89 

June. 


X 

.025 

— 

1.00 



53.OO 

July.. 


X 

.012 

= 

•47 


= 

24.91 

Aug.. 


X 

.0083 

— 

•33 


= 

17.49 

Sept. 


X 

.010 


.40 


= 

21.20 

Oct... 


X 

.015 

= 

.60 


— 

31.80 

Nov. 


X 

.040 

— 

1.60 


— 

84.80 

Dec. 

a 

X 

•0533 

-- 

2.14 



II3.42 




Total, 

16.00 

inches. 

Mean, 70.67 cu. ft. 

57. 

Ordinary 

Flow 

of 

Streams.- 

-Mr. 

Leslie has 


proposed * an arbitrary rule for computing the “average 
summer discharge” or “ordinary” flow of a stream, from 
the daily gaugings, as follows: 

“ Range the discharges as observed daily in their order 
of magnitude. 

“Divide the list thus arranged into an upper quarter, a 
middle half, and a lower quarter. 

“The discharges in the upper quarter of the list are to be 
considered as floods , and in the lower quarter as minimum 
floios. 

“For each of the gaugings exceeding the average of the 
middle half, including flood gaugings, substitute the average 
of the middle half of the list , and take the mean of the 
whole list, as thus modified, for the ordinary or average 
discharge , exclusive offlood-ivaters” 

This rule applied to a number of examples of actual 
measurements of streams in hilly English districts gave 
computed ordinary discharges ranging from one-fourtli to 


* Minutes of Proceedings of Institution of Civil Engineers, Vol. X, p. 327. 



















TABLES OF FLOW. 


81 


one-tliird of the measured mean discharge , including 
floods. 

The ordinary flow of New England streams is, at an 
average, equivalent to about one million gallons per day 
per square mile of drainage area, which expressed in cubic 
feet, equals about ninety-two cubic feet per minute per 
square mile. 

The above computation for the average flow in low cycle 
years gives a little less than eight-tenths of this amount, or 
seventy-one cubic feet per minute per square mile as the 
average flow throughout the year, and a little less than one- 
fourtli this amount as the minimum monthly flow* 

58. Tables of Flow Equivalent to Given Depths 
of Rain. —To facilitate calculations, tables giving the 
equivalents of various depths of monthly and annual rain¬ 
falls, in even continuous flow, in cubic feet per minute per 
acre, and per square mile, are here inserted. 

Greater or less numbers than those given in Tables 22 
and 23 may be found by addition, or by moving the decimal 
point; thus, from Table 22, for 40.362 inches depth, take 

Depth, 30 inches = 1590.204 cu. ft. 

10 “ = 530.068 “ 

.3 “ = 15.902 “ 

.06 “ = 3.180 “ 

.002 “ = .106 “ 

40.362 inches = 2139.460 cu. ft. 

To reduce the flows in the two tables to equivalent vol¬ 
umes of flow for like depths of rain in one day, divide the 
flows in Table 22 by 30.4369 (log. = 1.483400), and divide 
the flows in Table 23 by 365.2417 (log. = 2.562581). 

* Some useful data relating to tlie flow of certain British and Continental 
streams may be found in Beardmore’s “ Manual of Hydrology,” p. 149 (Lon- 
don, 1862 ). 







82 


FLOW OF STREAMS. 


TABLE No. 22. 

Equivalent Volumes of Flow, for given Depths of Rain in 

One Month* 


Depths of Rain 
in One Month. 

Equivalent Flow in 
Cubic Feet per 
Minute per Acre. 

Equivalent Flow in Cu¬ 
bic Feet per Minute 
per Square Mile. 

Equivalent Flow in Cu¬ 
bic Feet per Month per 
Square Mile. 

Inches. 

.OI 

.00083 

•530 

23,232 

.02 

.00166 

I.060 

46,464 

•°3 

.00248 

I *59° 

69,696 

.04 

.OO331 

2.120 

92,928 

•°5 

.OO414 

2.650 

I 16,160 

.06 

.OO497 

3 - i8 ° 

I 39>39 2 

.07 

.00580 

3.710 

162,624 

.08 

.00662 

4.240 

1^5,856 

.09 

.00745 

4.770 

209,088 

.1 

.00828 

5-3oo7 

232,320 

.2 

.01656 

10.6014 

464,640 

•3 

.02484 

15.9020 

696,960 

•4 

.03312 

21.2027 

929,280 

•5 

.04140 

26.5034 

1,161,600 

.6 

.04968 

31.8041 

I ?393?9 2 ° 

•7 

.05796 

37.1048 

1,626,240 

.8 

.06624 

42.4054 

1,858,560 

•9 

.07452 

47.7061 

2,090,880 

1.0 

.0828 

53.0068 

2,323,200 

2 

.1656 

106.0136 

4,646,400 

3 

.2484 

159.0204 

6,969,600 

4 

•33 1 2 

212.0272 

9,292,800 

5 

.4140 

265.0340 

11,616,000 

6 

.4968 

318.0408 

I 3?939?2oo 

7 

•5796 

371.0476 

16,262,400 

8 

.6624 

424.0544 

18,585,600 

9 

•7452 

477.0612 

20,908,800 

10 

.828 

530.068 

23,232,000 

20 

1.656 

1060.136 

46,464,000 

30 

2.484 

1590.204 

69,696,000 


* One month is taken equal to 30.4369 days. 















TABLES OF FLOW. 


83 


TABLE No. 2 3. 

Equivalent Volume of Flow, for given Depths of Rain in 

One Year.* 


Depths of Rain 
in One Year. 

Equivalent Flow in 
Cubic Feet per 
Minute per Acre. 

Equivalent Flow in Cu¬ 
bic Feet per Minute 
per Square Mile. 

Equivalent Flow in Cu¬ 
bic Feet per Year per 
Square Mile. 

Inches. 

.OI 

.000069 

.0442 

23,232 

.02 

.OOOI38 

.0883 

46,464 

•°3 

.000207 

•I 3 2 5 

69,696 

.04 

.OOO276 

.1767 

92,928 


.OOO345 

.2209 

I16,160 

.06 

.OOO414 

.2650 

I 39 > 39 2 

.07 

.OOO483 

.3092 

162,624 

.08 

.OOO552 

•3534 

185,856 

.09 

.000621 

•3976 

209,088 

.1 

.00069 

.4417 

232,320 

.2 

.OOI38 

.8834 

464,640 

♦3 

.00207 

i- 3 2 5 2 

696,960 

-4 

.00276 

1.7669 

929,280 

•5 

•OO345 

2.2086 

1,161,600 

.6 

.00414 

2.6503 

I > 393 > 9 2 ° 

•7 

.00483 

3.0921 

1,626,240 

.8 

.00552 

3-5338 

J , 85 8,5 60 

•9 

.00621 

3-9755 

2,090,880 

1.0 

.0069 

4 - 4 I 7 2 

2,323,200 

2 

.0138 

8.8345 

4,646,400 

3 

.0207 

13-2517 

6,969,600 

4 

.0276 

17.6689 

9,292,800 

5 

•0345 

22.0862 

11,616.000 

6 

.0414 

26.5034 

I 3 ? 939 ? 2 oo 

7 

.0483 

30.9206 

16,262,400 

8 

• 055 2 

35-3379 

18,585,600 

9 

.0621 

39 - 755 1 

20,908,800 

10 

.069 

44.1723 

23,232,000 

20 

.T38 

88.3447 

46,464,000 

3 ° 

.207 

132.5170 

69,696,000 

40 

.276 

176.6894 

92,928,000 

5 ° 

•345 

220.8617 

116,160,000 

60 

.414 

1 

265.0340 

i 39?39 2 j°oo 


* One year is taken, equal to 365 days, 5 hours, 49 minutes. 
















83a 


FLOW OF STREAMS. 


TABLE No. 23a. 

Statistics of Flow* of Sudbury River, Mass. 


Y ears. 

m 

00 

1876. 

1877. 

1878. 

1879. 

1880. 

Mean. 

Yearly rainfall, inches. 

45 - 49 ° 

49-563 

44.018 

57 - 93 1 

41.419 

38.177 

46.100 

Yearly flow in cubic feet per second per 


1.76 

00 

00 

H 


1.38 



square mile.. 

1.50 

2.25 

0.92 

1.615 

Percentage ot total rainfall flowing. 

44 • 88 

48.24 

57-90 

52.63 

45-33 

32 . 7 l 

47-56 

Inches ofrainfall flowing . 

20.418 

23.908 

25-487 

30.487 

18.775 

12.487 

21.927 

Minimum flow in any month in cubic feet per 


0.28 






second per square mile. 

0.16 

0.09 

0.20 

O. IT 

0.13 

.... 

Minimum flow in any week in cubic feet per 


0.080 

0.036 





second per square mile. 


0.105 

• • • • 

• • • • 

• • • • 

Minimum flow in any day in cubic feet per 




15.61 

21.36 



second per square mile. 

19.30 

41-39 

22.08 

.... 

• . . . 

Rainfall in July, August, September and 
October, inches. 

17.380 

17.709 

I 54 - 7 1 

17.616 

13.129 

15-624 

16.155 

Inches of rain flowing in July, August, Sep- 








tember and October. 

0.60 

0-39 

0-39 

0.50 

0.30 

0.19 

1.40 

Percentage of rain flowing in July, August, 


11.67 





September and October.. 

16.05 

10.08 

12.92 

IO.32 

5-55 

IX. 22 

Flow in July, August, September and Octo- 



1.805 



0.867 


ber, in cubic feet per second per square mile 

2.790 

1.784 

2.276 

1-355 

1.813 


TABLE No. 23b 


Summary of Rainfall on the Sudbury Basin. 


Year. 

January. 

February. 

March. 

April. 

May. 

June. 

July. 

August. 

September. 

October. 

November. 

December. 

1875. 

2.420 

3-^50 

3 - 74 o 

3-230 

3-560 

6.240 

3-570 

5 - 53 ° 

3-430 

4.850 

4.830 

0.940 

1876. 

1.830 

4.210 

7-430 

4.197 

2.763 

2.040 

9-134 

1.720 

4.614 

2.241 

5-764 

3.620 

1877. 

3.216 

0-739 

8 357 

3-435 

3.702 

2.425 

2-951 

3.682 

0.323 

8.515 

5.803 

0.870 

1878. 

5.632 

5-973 

4.689 5.790 

0.956 

3-884 

2.971 

6-937 

I .291 

6.417 

7.024 

6.367 

1879. 

2.478 

3-562 

5. ^0 4.716 

i -579 

3-789 

3-933 

6.509 

1.878 

0.809 

2.682 

4-344 

1880. 

3-566 

3.980 

3.31513.105 

1.836 

2.138 

6.273 

4.008 

1.603 

3-740 

1.785 

2.828 

Mean. 

3 -* 9 ° 

3.602 

5.4454.129 

2-399 

3 - 4 i 9 

4.805 

4-731 

2.190 

4.429 

4.648 

3.162 

Minimum. 

1.830 

0-739 

3.315 3.105 

0.956 

2.040 

2.951 

1.720 

0.323 

0.809 

1 • 785 

0.870 

Maximum. 

3-566 

5-973 

8-357 

5-790 

3 • 7°2 

6.240 

9-134 

6-937 

4.614 

8.515 

7.024 

6.367 

Ratio of monthly mean... 

0.829 

0.936 

1.416 

1.074 

0.624 

0.863 

1.249 

I .227 

0.569 

1.152 

1.208 

0.822 


* Data selected from a “ Descriptive Report on an additional supply of Water 
to Boston from Sudbury River,” by A. Fteley, resident Engineer, Boston, 1882. 













































































TABLES OF FLOW 


83 b 


TABLE No. 23c. 


Percentage of 


Rainfall flowing from the Sudbury Basin. 


Y EAR. 

January. 

February. 

March. 

April. 

May. 

June. 

July. 

August. 

September. 

October. 

November. 

December. 

1875 . 

7.60 

76.54 

76.52 

162.94 

59-52 

24.05 

16.05 

12.77 

10.44 

23-75 

46.54 

110.74 

1876. 

62.68 

54.20 

106.47 

i 35 - 4 i 

73 - 5 i 

18.77 

3-57 

42.03 

6.89 

18.61 

32.58 

22.35 

1877. 

36.50 

206.90 

102.74 

120 .2Q 

67.04 

42.52 

12.20 

5-87 

31.89 

r 3- 2 4 

42.17 

264.37 

1878. 

57-32 

66.50 

133-42 

48.48 

260.15 

22.48 

7.71 

12.22 

21.46 

14-35 

41.60 

89.01 

1879 .• 

50.40 

77-37 

80.86 

114.06 

125.84 

18.82 

7.14 

10.83 

12.94 

15-57 

13-24 

j 8-99 

1880. 

57-43 

76.82 

75.80 

66.62 

51 -22 

14-52 

5-14 

5-42 

8.86 

4-97 

20.35 

11 -33 

Mean . 

45 - 3 2 

93.06 

95-97 

107.96 

106.21 

23-58 

8.64 

14.86 

i 5 - 4 i 

15.08 

32.75 

86.13 

Minimum. 

7.60 

54.20 

75.80 

48.48 

51.22 

14-52 

3.57 

5-42 

6.89 

4-97 

13-24 

n -33 

Maximum. 

Ratio of monthly 

62.68 

206.90 

I 33-42 

162.94 

260.15 

42.52 

16.05 

42.03 

31.89 

2 3-75 

46.54 

264-37 

mean. 

0.84 

i -73 

1.79 

2.02 

I.98 

0.44 

0.16 

O 

to 

OO 

0.29 

0.28 

0.61 

i 60 


TABLE No. 23d. 


Volume of Flow from the Sudbury Basin. 

(In Cubic Feet per Minute per Square Mile.) 


Year. 

January. 

February. 

March. 

April. 

» 

1875. 

10.13 

147-43 

158.08 

300.47 

1876. 

56.24 

119.62 

387-87 

287.93 

1877. 

57-46 

83-03 

420.99 

205.97 

1878. 

158.25 

215.61 

306.73 

142.20 

1879. 

61.62 

150.54 

205.03 

274.18 

1880. 

98-53 

I 57-24 

120.89 

102.83 

Mean . 

73 • 7 1 

I 45-58 

266.60 

218.93 

Minimum. 

10.13 

83-03 

120.89 

102.83 

Maximum. 

158.25 

215.61 

420.99 

300.47 

Ratio of monthly 
mean. 

0.79 

i -57 

to 

00 

2.36 


May. 

June. 

July. 

August. 

September. 

October. 

November. 

December. 

118.37 

85.70 

31.66 

38.99 

20.44 

63.66 

128.32 

57-52 

99-55 

19-39 

16.11 

34 - 3 i 

16.12 

20.42 

95-'4 

39-65 

121.69 

52.22 

17.63 

10.59 

5-21 

55-23 

123.98 

112.79 

121.95 

44-23 

n.23 

41.61 

14.06 

45.14 

148.04 

277.86 

98.01 

36.37 

13-85 

34-43 

12.39 

6.22 

18.07 

40.69 

45-24 

15-43 

15-52 

10.45 

7.06 

8.94 

18.06 

i 5 - 4 i 

100.80 

42.19 

16.83 

29.40 

12.54 

33.27 

88.60 

84.32 

45-24 

15-43 

ir.23 

10.45 

5.21 

6.22 

18.06 

i 5 - 4 i 

121.95 

85.70 

31 -66 

4I.6l 

20.44 

63.66 

148.04 

277.86 

1.09 

0-45 

0.18 

0.32 

0.14 

0.36 

0.96 

0.91 


On the 26tli of March, 1876, the average volume of flow 
in the river for 24 hours was estimated to be equivalent to 
a depth 1.6 in. of rain over the entire water shed, or 43 cu. ft. 
per sec. per sq. mile, and this was considered an extraordi¬ 
nary freshet. 





















































































CHAPTER V. 

STORAGE AND EVAPORATION OF WATER. 

STORAGE. 

59. Artificial Storage.— The fluctuations of the rain¬ 
fall, flow of streams, and consumption of water in the differ¬ 
ent seasons of the year, require almost invariably that, for 
gravitation and hydraulic power pumping supplies , there 
shall be artificial storage of tlie surplus waters of the sea¬ 
sons of maximum flow, to provide for the draught during 
the seasons of minimum flow. A grand exception to this 
general rule is that of the natural storage of the chain of 
great lakes that equalizes the flow of the St. Lawrence 
River, which furnishes the domestic water supply of the 
City of Montreal and the hydraulic power to pump the same 
to the reservoir on the mountain. 

When the mean annual consumption, whether for do¬ 
mestic use, or for power and domestic use combined is 
nearly equal to the mean annual flow of the supplying 
watershed, the question of ample storage becomes of su¬ 
preme importance. The chief river basins of Maine present 
remarkable examples of natural storage facilities, since 
they have from six to thirteen per cent., respectively, of 
their large watershed areas in pond and lake surfaces. 

GO. Losses Incident to Storage.— There are losses 
incident to artificial storage that must not be overlooked; 
for instance, the percolation into the earth and through the 
embankment, evaporation from the reservoir surface and 
from the saturated borders, and in some instances constant 
draught of the share of riparian owners. 


EMBANKMENT: IMPOUNDING AND DISTRIBUTING RESERVOIR, NORWICH, CONN. 













/ 































































RIGHTS OF RIPARIAN OWNERS. 


85 


61. Sub-strata of the Storage Basin. —The structure 
of the impounding basin, especially when the water is to 
till it to great height above the old bed, is to be minutely 
examined, as the water at its new level may cover the edges 
of porous strata cropping out above the channel, or may 
find access to fissured rocks, either of which may lead the 
storage by subterranean paths along the valley and deliver 
it, possibly, a long distance down the stream, or in a mul¬ 
titude of springs beyond the impounding dam. If the 
water carries but little sediment of a silting nature, this 
trouble will be difficult to remedy, and liable to be serious¬ 
ly chronic. 

62. Percolation from Storage Basins.— Percolation 
through the retaining embankment is a result of slighted or 
unintelligent construction, and will be discussed when con¬ 
structive features are hereafter considered. (See Reservoir 
Embankments.) 

63. Rights of Riparian Owners. — The rights of 
riparian owners, ancient as the riparian settlements, to the 
use of the water that flows, and its most favored piscatory 
produce, is often as a thorn in the impounder’s side. What 
are those rights ? The Courts and Legislatures of the man¬ 
ufacturing States have wrestled with this question, their 
judges have grown hoary while they pondered it, and their 
attorneys have prospered, and yet who shall say what 
riparian rights shall be, until the Court has considered all 
anew. 

Beloe mentions * that it is a “common (British) rule in 
the manufacturing districts to deduct one-sixtli the average 
rainfall for loss by floods, in addition to the absorption and 
evaporation, and then allow one-tliird of the remainder to 


* Beloe on Reservoirs, p. 12. London, 1872. 





86 


STORAGE AND EVAPORATION OF WATER. 


the riparian owners, leaving two-thirds to the impounders. 
In some instances this is varied to the proportion of one- 
quarter to the former and three-quarters to the latter.” 

The question can only be settled equitably upon the 
basis of daily gaugings of How, through a long series of 
years. A theoretical consideration involves a thorough 
investigation of its geological, physical, and meteorological 
features. There is no more constancy in natural flow at any 
season than in the density of the thermometer’s mercury. 
The flow increases as the storms are gathered into the chan¬ 
nel, it decreases when the bow has appeared in the heavens ; 
it increases when the moist clouds sweep low in the valleys, 
it decreases under the noonday sun ; it increases when the 
shadows of evening fall across the banks, it decreases when 
the sharp frosts congeal the streams among the hills. 

64. Periodical Classification of Riparian Rights. 
—The riparian rights subject to curtailment by storage 
might be classified by periods not greater than monthly, 
though this is rarely desirable for either party in interest, 
but they should be based upon the most reliable statistics 
of monthly rainfall, evaporation, and flow, as analyzed and 
applied with disciplined judgment to the particular locality 
in question. 

65. Compensations.— In the absence of local statistics 
of flow, it may become necessary, in settling questions of 
riparian rights, or adjusting compensation therefor, to esti¬ 
mate the periodic flow of a stream by some such method as 
is suggested above in the general discussion upon the flow 
of streams, after which it remains for the Court to fix the 
proportion of the flow that the impounders may manipulate 
for their own convenience in the successive seasons, and the 
proportion that is to be passed down the stream regularly 
or periodically. 


EVAPORATION PHENOMENA. 


87 


EVAPORATION. 

G6. Loss from Reservoir by Evaporation. —Losses 
by evaporations from tlie surfaces of shallow storage reser¬ 
voirs, lakes and ponds are, in many localities, so great in the 
summer and autumn that their areas are omitted in compu¬ 
tations of water derivable from their watersheds. This is a 
safe practice in dry, warm climates, in which the evapora¬ 
tions from shallow ponds may nearly or quite equal the 
volume of rain that falls directly into the ponds. Marshy 
margins of ponds are profligate dispensers of vapor to the 
atmosphere, usually exceeding, in this respect the water 
surfaces themselves. 

G7. Evaporation Phenomena.— Evaporation is the 
most fickle of all the meteorological phenomena, and its 
action is so subtle that we cannot observe its processes. Its 
results demonstrate that the constituents of water are con- 
stantly changing their state of existence from that of gas to 
liquid, liquid to gas, liquid to solid, and solid to gas. The 
action takes place as well upon polar ice fields or mountain 
snows, as upon tropical lagoons, though less in degree. 
The active vapors that form within the waters or porous ice, 
silently emerge through their surfaces and proceed upon 
their ethereal mission, and are not again recognizable until 
they have been once more united into cloud and condensed 
into rain. 

The rapidity with which water, snow, and ice are con¬ 
verted into vapor and pass off by evaporation is depend¬ 
ent upon the temperature of the waiter and atmosphere, but 
more especially upon their relative temperatures, and upon 
the dryness and activity of the atmosphere. The formation 
of vapor in a body of water is supposed to be at its mini¬ 
mum when the atmosphere is moist and the atmosphere 


88 STORAGE AND EVAPORATION OF WATER. 

* 

and water are quiet and of an equal low temperature, and 
most active when the atmosphere is dryest and hottest and 
the wind brisk and water warm. 

M. Aime Drian observed that “when the temperature 
of the dew point is higher than that of the evaporating sur¬ 
face, water is deposited on that surface,” which action he 
styles negative evaporation. 

Undoubtedly the cool surfaces of deep waters condense 
moisture in summer from warm moist atmospheres wafted 
across them, and thus at times are gaining in volume while 
popularly supposed to be losing by evaporation. When 
winds blow briskly across a water surface, large volumes 
of unsaturated air are presented in rapid succession to 
attract its vapors, and the wave motion increases the agita¬ 
tion of the body and permits its vapors to escape freely. 

The atmosphere has, however, its limit of power to ab¬ 
sorb vapor for each given temperature, and when it is fully 
saturated it can receive no more without depositing an equal 
amount, or until its temperature is raised. 

08. Evaporation from Water.— In an instructive 
paper upon rainfall and evaporation, by Mr. A. Golding, 
State Engineer at Copenhagen, quoted* by Beardmore, we 
find some valuable measurements of evaporation in the 
different seasons, from which the following, relating to 
evaporation at Emdrup, is extracted. 


* Vide Beardmore’s Hydrology, p. 269 d. London, 1862. 



EVAPORATION FROM EARTH. 


89 


TABLE No. 24. 

Evaporation from Water at Emdrup, Denmark. 

N. Lat. 55°4i // ; E. Long i2°34" from Greenwich. 


Year. 

d 

d 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

hb 

p 

< 

Sept. 

Oct. 

Nov. 

Dec. 

Total. 


In . 

In . 

In . 

In . 

In . 

In . 

In . 

In . 

In . 

In . 

In . 

In . 

In . 

1849 

1.1 

o-3 

1.8 

2.5 

4.1 

5-8 

4-7 

4.0 

2.6 

I.I 

0.9 

0.6 

2 9-5 

1850 

I.I 

o-3 

1.2 

i-7 

4-5 

5-6 

4.8 

4.8 

2.4 

1.6 

0.9 

0.2 

29.1 

1851 

°-5 

0.4 

0.7 

i-7 

4.2 

4.8 

5-7 

5-i 

2.7 

i-5 

0.6 

o-5 

28.4 

1852 

0.7 

o-5 

0.8 

2.4 

3-8 

. 4.6 

6.4 

4-5 

2.7 

i-7 

0.8 

o-5 

29.4 

1853 

o-5 

o.x 

0.7 

1.0 

4.1 

6.2 

5-i 

4.2 

2.8 

1.1 

0.6 

o-5 

26.9 

1854 

o-5 

0.9 

0.9 

3-2 

3-3 

4-5 

5-2 

4-3 

2.6 

1.2 

°-7 

0.6 

27.9 

1855 

1.0 

1.1 

o-5 

1.2 

2.6 

4.1 

4-7 

4.x 

2.8 

1.4 

0.9 

0.7 

25-1 

1856 

o-5 

o-5 

1.2 

2.1 

2.8 

4.6 

4-3 

4.0 

2.0 

0.9 

0.6 

°-5 

24.0 

1857 

0.7 

0.6 

0.6 

1.4 

4.1 

6.6 

5-9 

4-3 

3-2 

1.4 

0.7 

0.4 

29.9 

1858 

0.4 

0.7 

1.2 

3-i 

5-1 

6.1 

4.9 

5-6 

2.8 

1.6 

0.7 

0.4 

30.6 

1859 

o-3 

o-5 

°-7 

1.9 

4-3 

5-8 

5-3 

3-8 

1.8 

1.0 

0.7 

o-3 

26.4 

Mean .. 

0.7 

o-5 

0.9 

2.0 

3-9 

5-3 

5-2 

4.4 

2.6 

i-3 

0.7 

0.5 

27.9 

Ratio .. 

.301 

.215 

•3 8 7 

.860 

1.592 

2.323 

2.237 

1.892 

1.118 

•559 

.301 

.215 

.... 


Mean Evaporation from Short Grass, 1852 to 1859 inclusive. 

Mean..| 0.7 | 0.8 | 1.2 | 2.6 | 4.1 [ 5.5 | 5.2 | 4.7 | 2.8 | 1.3 | 0.7 | 0.5 | 30.1 

Mean Evaporation from Long Grass, 1849 to 1856 inclusive. 

Mean.. | 0.9 | 0.6 | 1-4 • | 2.6 | 4.7 | 6.7 [ 9.-3 | 7.9 [ 5.2 | 2.9 | 1.3 | 0.5 | 44.0 

Mean Rainfall at same Station, 1848 to 1859 inclusive. 

Mean.. I 1.5 I 1.7 I 1.0 I 1.6 ( 1.5 I 2.2 I 2.4 I 2.4 I 2.0 I 2.3 I 1.8 I 1.5 I 21.9 


TABLE No. 25. 

09. Evaporation from Earth. —Mean Evaporation from 
Earth, at Bolton Le Moors,* Lancashire, Eng., 1844 to 

1853, INCLUSIVE. 

Lat. 53°3o" N.; Height above the Sea, 320 Feet. 



d 

d 
>—> 

A 

4 J 

A 

c 3 

S 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Total. 

Mean .. 
Ratio... 

0.64 

.299 

0 - 95 . 

•444 

i -59 

•739 

2-59 

1.212 

4-38 

2.049 

3-84 

1.796 

4.02 

1.887 

3.06 

M 3 1 

2.02 

•945 

1.28 

•599 

0.81 

•379 

O.47 

.220 

25-65 


Mean Rainfall at same Station, 1844 to 1853 inclusive. 

Mean..] 4.63 | 4.03 j 2.25 J 2.22 | 2.23 | 4 | 4-32 | 4-77 | 3-79 | 5-°7 | 4-64 | 3-94 | 45-96 


* Beardmore’s Hydrology, p. 325. 





























































































90 STORAGE AND EVAPORATION OF WATER. 


Mean Evaporation from Earth, at Whitehaven, Cumberland, 

Eng., 1844 to 1853 inclusive. 

Lat. 54'"'30" N. ; Height above the Sea, 90 feet. 



Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

1 

Oct. 

Nov. 

Dec. 

Total. 

Mean. 
Ratio .. 

o -95 

• 39 ° 

I.OI 

.415 

1.77 

.727 

2.71 

I.II 3 

4 .ii 

1.689 

4-25 

1.746 

4- T 3 

1.697 

3- 2 9 

i -352 

2.96 

1.216 

1.76 

•723 

1-25 

• 5 i 3 

1.02 

.419 

29.21 


Mean Rainfall.at same Station, 1844 to 1853 inclusive. 

Mean.. | 5.1 | 3.4 | 2.5 j 2.2 | 1.9 | 3.1 | 4.3 | 4.3 | 3.1 | 5.3 | 4.5 | 3.8 [ 43 . 5 


70. Examples of Evaporation.— Charles Greaves, 
Esq., conducted a series of experiments upon percolation 
and evaporation, at Lee Bridge, in England, continuously 
from 1860 to 1873, and lias given the results * to the Insti¬ 
tution of Civil Engineers. The experiments were on a large 
scale, and the very complete record is apparently worthy 
of full confidence. 

The evaporation boxes were one yard square at the sur¬ 
face and one yard deep. Those for earth were sunk nearly 
flush in the ground, and that for water floated in the 
river Lee. The mean annual rainfall during the time was 
27.7 inches. The annual evaporations from soil were, mini¬ 
mum 12.067 inches; maximum 25.141 inches; and mean 
19.534 inches:—from sand , minimum 1.425 inches; maxi¬ 
mum 9.102 inches; and mean 4.648 inchesfrom water, 
minimum 17.332 inches; maximum 26.933 inches; and 
mean 22.2 inches. 

Some experimental evaporators were constructed at 
Dijon on the Burgundy canal, and are described in Annales 
des Fonts et Chausses. They are masonry tanks lined 
with zinc, eight feet square and one and one-tliird feet deep, 


* Trans. Inst. Civil Engineers, 1876, Vol. XLV, p. 33. 


































RATIOS OF EVAPORATION. 


91 


and are sunk in the ground. From 1846 to 1852, there was 
a mean annual evaporation of 26.1 inches from their water 
surfaces against a rainfall of 26.9 inches. At the same time 
a small evaporator, one foot square, placed near the larger, 
gave results fifty per cent, greater. 

Observations of evaporation from a water surface at the 
receiving reservoir in New York indicated the mean annual 
evaporation from 1864 to 1870 inclusive as 39.21 inches, 
whicli equaled 81 per cent, of the rainfall. 

On the West Branch of the Croton River, an apparatus* 
was arranged for the purpose of measuring the evaporation 
from water surface, consisting of a box four feet square and 
three feet deep, sunk in the earth in an exposed situation 
and filled with water. The mean annual evaporation was 
found to be 24.15 inches, or about fifty per cent, of the 
rainfall. The observations were made twice a day with 
care. The maximum annual evaporation was 28 inches. 

Evaporations from the surface'of water in shallow tanks 
are variously reported as follows : 


At 

Cambridge, Mass., 

one 

year, 

56.00 inches depth, 

<< 

Salem, “ 

u 

u 

56.00 

u 

u 

Syracuse, N. Y., 

a 

it 

50.20 “ 

a 

a 

Ogdensburgh, N. Y., 

a 

a 

49-37 “ 

u 

a 

Dorset, England, 

three 

a 

25.92 

a 

u 

Oxford, “ 

five 

u 

3 r -°4 

u 

a 

Demerara, 

three 

a 

35 - 12 

a 

it 

Bombay, 

five 

u 

82.28 “ 

a 


71. Ratios of Evaporation.— In the eastern and mid-j 
die United States, the evaporation from storage reservoirs, 1 
having an average depth of at least ten feet, will rarely 
exceed sixty per cent, of the rainfall upon their surface. 


* Vide paper on “ Flow of the West Branch of the Croton River,” by J. Jas. 
R. Croes. Trans. Am. Soc. Civ. Engrs., July, 1874, p. 83. 




92 


STORAGE AND EVAPORATION OF WATER. 


The ratio of evaporation in each month to the monthly aver¬ 
age evaporation, or one-twelfth the annual depth, is esti¬ 
mated to b6, for an average, approximately as follows : 


TABLE No. 26. 

Monthly Ratios of Evaporation from Reservoirs. 



d 

d 
*— > 

Feb. 

Mar. 

U 

Q-i 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean ratio.... 

•3° 

•35 

•5° 

.80 

i-45 

0 

H 

1.85 

2.00 

i-45 

•75 

•50 

•35 


The following ratios of the annual evaporation from 
water surfaces are equivalent to the above monthly ratios, 
and may be used as multipliers directly into the annual 
evaporation to compute an equivalent depth of rain in 
inches upon the given surface in action. Beneath the ratios 
are given the equivalent depths for each month of 40 inches 
annual rain, assuming the annual evaporation to equal 
sixty per cent, of the rainfall, or 24 inches depth. 


TABLE No. 2 7. 

Multipliers for Equivalent Inches of Rain Evaporated. 



C 

oj 

Feb. 

Mar. 

Apr. 

May. 

June. 

3 - 
•—» 

Aug. 

Sept. 

L 

CJ 

0 

> 

0 

£ 

Dec. 

Ratio of annual evapora¬ 
tion . 

Equivalent depth of rain 


.0292 

.0417 

.0667 

.1208 

.1417 

• 1542 

.1667 

.1208 

.0625 

.0417 

.0292 

—inches. 

.6 

•7 

1.0 

1.6 

2.9 

3-4 

3-7 

4 - 

2.9 

i -5 

1.0 

•7 


* 42 . Resultant Effect of Rain and Evaporation.— 

For the purpose of comparing the effects upon a reservoir 
replenished by rain only, let us assume the available rain¬ 
fall to be eight-tenths of 40 inches per annum, and the 
ratios of mean monthly rain, and the ratios of annual rain 
in inches depth, to be as per the following table: 






























































PRACTICAL EFFECT UPON STORAGE. 


93 



fl 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

bi) 

3 

Sept. 

Oct. 

Nov. 

Dec. 

Ratio of aver, 
monthly rain 

•75 

•83 

.90 

1.10 

1.30 

1.08 

1.12 

1.20 

1.00 

•95 

•93 

.84 

Ratio of .8 of 










annual rain. 

.0625 

.0692 

.0750 

.0917 

.1083 

.0900 

•0933 

.IOOO 

•0833 

.0792 

•0775 

.O7OO 

Equiv. inches 










of rain. 

2.00 

2.21 

2.40 

2-93 

3-47 

2.88 

2.99 

3.20 

2.67 

2-53 

2.48 

2.24 


Comparing, in tlie two last tables, and tlieir lowest 
columns, the inches of gain by rainfall npon the reservoir, 
supposing the sides of the reservoir to be perpendicular, and 
the inches of loss from the same reservoir by evaporation, 
we note that the gain preponderates until June, then the 
loss preponderates until in November. 

73. Practical Effect upon Storage. —Since the prac¬ 
tical value of storage is ordinarily realized between May 
and November, the excess of loss during that term is, 
practically considered, the annual deficiency from the reser¬ 
voir chargeable to evaporation. We compute its maximum 
in the following table, commencing the summation in June, 
all the quantities being in inches depth of rain. 



d 

Feb. 

Mar. 

Apr. 

May. 

June. 

July. 

hi 

3 

<3 

Sept. 

O 

O 

Nov. 

Dec. 

Gain by rain— 
inches . 

2.00 

2.21 

2.40 

2.93 

3 47 

2.88 

2.99 

3.20 

2.67 

2*53 

2.48 

2.24 

Loss by evapo¬ 
ration—inches 

.60 

.70 

1.00 

1.60 

2.90 

3 - 4 o 

3-70 

4.00 

2.90 

1.50 

1.00 

O.7O 

D i ff e r e n c e— 

inches. 

+ I.40 

+1.51 

+1.40 

+ i -33 

+ 0.57 

—0.62 

—0.71 

—0.80 

—0.23 

+ 0.97 

+1.48 

+ I -54 

Max. deficiency 
after June — 
inches . 

.... 

.... 

... 


.... 

—0.62 

I *33 

-2.13 

—2.36 

—i -39 

+ 0.09 

.... 


If the classification is reduced to daily periods instead 
of monthly, the maximum deficiency, according to the 
above basis, will in a majority of years exceed three inches. 






























































CHAPTEB VI. 


SUPPLYING CAPACITY OF WATERSHEDS. 

74. Estimate of Available Annual Flow of Streams. 

—Applying our calculations in the last chapter, of available 
flow of water from the unit of watershed, one square mile, 
and modifying it by the elements of compensation, storage, 
evaporation, and percolation, we then estimate mean annual 
quantities of low-cycle years, applicable to domestic con¬ 
sumption, as follows: 

Assumed mean annual rainfall. 40 inches. 

Flow of stream available for storage, 40 per cent, of mean rain = 16 inches of rain. 

This available rain is applied to : 

1st. Compensation to riparian owners, say 16.8 p. c. of mean rain = 6.72 in. of rain. 

2d. Evaporation from surface of storage reservoir, “ 2.4 “ “ 11 “ = .96“ “ “ 

3d. Percolation from storage reservoir, “ 2.4 “ “ “ = .96 “ “ “ 

4th. Balance available for consumption, 18.4 “ “ “ “ = 7.36 “ “ “ 

Total. 40 per cent. 16 inches. 

The 7.36 inches of rain estimated as available from a 
40-inch annual rain equals 17,098,762 cubic feet of water, 
which is equivalent to a continuous supply of seven cubic 
feet per day (= 52.36 gals.) each, to 6,692 persons. 

By applying to the annual results the monthly ratios, 
and thus developing the monthly surpluses or deficiencies 
of how, we shall have in the algebraic sum of the deficien¬ 
cies the volume of storage necessary to make forty per cent, 
of the rainfall available, and this storage must ordinarily 
approximate one-tliird of the annual how available for 
storage. 








(Constructed in 1836,) 






















































































































































































































































MONTHLY AVAILABLE STORAGE REQUIRED. 95 

75. Estimate of Monthly Available Storage Re¬ 
quired. —Computation of a supply, and the required 
storage ; applied to one square mile of watershed as a unit 
of area. 

Assumed data: Population to be supplied, 6,500 per¬ 
sons, consuming 7 cubic feet per capita daily, each ; 

Mean annual rainfall, 40 inches, and eight-tenths = 
32 inches of rain, in the low-cycle years ; 

Available How of stream, fifty per cent, of eight-tenths 
of rain = 16 inches ; 

Compensation each month, .168 of one-twelfth the mean 
annual depth of rain = .56 inches each month uniformly; 

Evaporation annually from the reservoir surface only, 
sixty per cent, of the depth of mean annual rain, or 24 
inches; and monthly, sixty per cent, of one-twelftli the 
annual evaporation = 2 inches. 

Area of storage reservoir, .04 square mile,* or 25.6 acres, 
with equivalent available draught of ten feet for that sur¬ 
face. The evaporation of two inches from four hundredths 
of a square mile = .08 inch from one square mile. 

Volume of percolation assumed to equal volume of 
evaporation from the reservoir surface. 

The monthly ratios will be multiplied into 


40 in. x .8 x .50 p. c. _ 


.168 X 


12 months 
40 in. mean rain 


12 months 


: 1.3333 f° r the monthly flow. 

= .56 in. for monthly compensation. 


.04 x 


40 in. x 60 p. c. 
12 months 


— .08 in. for monthly evaporation from reservoir. 


“ — .08 in. for monthly percolation from reservoir. 

6500 x 7 cu. ft. X 30.4369 clays = 1,384,879 cu. ft. for monthly con¬ 
sumption. 


* A unit of reservoir area, for each square mile unit of watershed. 











96 


SUPPLYING CAPACITY OF WATERSHEDS. 


TABLE No. 28. 

Monthly Supply to, and Draft from, a Storage Reservoir. 


Month. 

Monthly 

Flow. 

Monthly 

Compen¬ 

sation. 

Monthly 
Evapora¬ 
tion from 
Reser- 

Monthly 
Percola¬ 
tion FROM 
Reser- 

Monthly 

Domestic 

Consump¬ 

tion. 

Surplus. 

Deficiency. 



cubic feet. 

cubic feet. 

VOIR. 

cubic feet. 

VOIR. 

cubic Jeet. 

cubic feet. 

cubic feet. 

cubic feet. 



Gain. 

Loss. 

Loss. 

Loss. 

Used. 



Jan. 

| 

Ratio, 1.65 
5,111,040 

Ratio, .168 
1,300,992 

Ratio, .30 
cc 7£7 

Ratio, .30. 

CC 7 C 7 

Ratio, 1.05 

T A C A T 0 Q 

2,244,411 




j jyJ j 1 


A >4 j 4 ' 1 - j 


Feb. 


Ratio, 1.50 
4,646,400 

.168 

1 , 300,992 

•35 

65,050 

•35 

65,050 

1.10 

1,523,367 

1,691,941 





Mar. 

| 

Ratio, 1.65 
5,111,040 

.168 

1,300,992 

•50 

92,928 

•50 

92,928 

.90 

1,246,391 

2,377,801 





Apr. 

| 

Ratio, 1.45 
4,491,520 

.168 

1,300,992 

.80 

148,685 

.80 

148,685 

.85 

1,177,147 

1,728,011 





May 


Ratio, .85 
2,632,960 

.168 

1,300,992 

I *45 

269,491 

i -45 

269,491 

.90 

1,246,391 


453,405 




June 

| 

Ratio, .75 

2,323,200 

.168 

1,300,992 

1.70 

315,955 

'I.70 

315,955 

1.00 

1,384,879 


994,581 




July 

| 

Ratio, .35 
1,084,160 

.168 

1,300,992 

1.85 

343,834 

1.85 

343,834 

1.20 

1,661,855 


2 , 566,355 




Aug. 

1 

Ratio, .25 

774,400 

.168 

1,300,992 

2.00 

371,712 

2.00 

371,712 

1-25 

1,731,099 


3,001,115 



Sept. 

| 

Ratio, .30 
929,280 

.168 

1,300,992 

i -45 

269,491 

i -45 

269,491 

1.05 

1,454,123 


2,364,817 




Oct. 

| 

Ratio, .45 
1,393,920 

.168 

1,300,992 

•75 

I 39 , 39 2 

•75 

I 39 , 39 2 

.90 

1,246,391 


1,432,247 




Nov. 

| 

Ratio, 1.20 
3 , 717,120 

.168 

1,300.992 

•50 

92,928 

•50 

92,928 

•85 

1,177,147 

1 , 053,125 





Dec. 

| 

Ratio, 1.60 
4,956,160 

.168 

1,300,992 

•35 

65,050 

•35 

65,050 

•95 

1,315,635 

2,209,433 





Totals 

37,171,200 

15,611,904 

2,232,072 

2,230,278 16,618,548 

11,299,722 

10,812,520 


From certain localities no claim will arise for diversion 
of the water, or the diversion may be compensated for by 
the payment of a cash bonus, in which case the proportion 
of rainfall applicable to domestic consumption will be a 
little more than doubled, and approximately as follows, 
neglecting percolation from the storage reservoir. 















































MONTHLY AVAILABLE STORAGE REQUIRED. 


97 


The monthly ratios will here be multiplied into 
40 in. x .8 x .50 p. c. 


12 months 
40 in. x .60 p. c. 


— I -3333 i n - t° r the monthly flow. 

.04 x -- ' , r - = .08 in. for monthly evaporation from reservoir. 

12 months r 

13,500 persons x 7 cu. ft. x 30.4369 days = 2,876,287 cu. ft. for 

monthly consumption. 


TABLE No. 29 . 

Monthly Supply to, and Draft from, a Storage Reservoir 

(without compensation). 


Month. 

Monthly 

F LOW. 

cubic feet. 

Monthly 

Evaporation 

from 

Reservoir. 
cubic feet. 

Monthly 

Domestic 

Consumption. 

cubic feet. 

Surplus. 

cubic feet. 

Deficiency. 

cubic feet. 

Jan. | 

Gain. 

Ratio, 1.65 
5,111,040 

Loss. 

Ratio, .30 

57,557 

Used. 

Ratio, 1.05 
3,020,101 

2,102,889 


Feb. | 

Ratio, 1.50 
4,646,400 

•35 

65,050 

I. IO 

3,163,916 

1 , 417,432 


Mar. j 

Ratio, 1.65 
5,111,040 

•50 

92,928 

.90 

2,588,658 

2,429,454 


Apr. 

Ratio, 1.45 
4,491,520 

.80 

148,685 

.85 

2 , 444,844 

1,897,991 


May | 

Ratio, .85 
2,632,960 

1 45 

269,491 

.90 

2,588,658 


225,189 

June 

Ratio, .75 
2,323,200 

1.70 

315,955 

I.OO 

2,876,287 


869,042 

July | 

Ratio, .35 
1,084,160 

1.85 

343,834 

1.20 

3 , 45 L 544 


2,711,218 

Aug. | 

Ratio, .25 
734,400 

2.00 

371,712 

1-25 

3 , 595,359 


3,232,671 

Sept. | 

Ratio, .30 
929,280 

i -45 

269,491 

1.05 

3,020,101 


2,360,312 

Oct. j 

Ratio, .45 

!, 393 , 9 2 ° 

•75 

I 39 , 39 2 

.90 

2,588,656 


L 334 ,I 30 

Nov. -j 

Ratio, 1.20 
3,717,120 

.50 

92,928 

.85 

2,444,844 

1 , 179,348 


Dec. j 

Ratio, 1.60 
4,956,160 

•35 

65,050 

•95 

2,732,472 

2,158,638 


Totals, 

37,171,200 

2,232,072 

34,515,442 

11,185,754 

10,732,562 


7 









































98 


SUPPLYING CAPACITY OF WATERSHEDS. 


7G. Additional Storage Required. — Forty inches 
of rainfall on one square mile equals a volume of 92,928,000 
cubic feet. The deficiency as above computed is nearly 
twelve per cent, of this quantity, and calls for an available 
volume of water in store early in May, or at the beginning 
of a drought, equal to about one-eighth the mean annual 
rainfall. 

The calculations of supply and draught in the two 
monthly tables given above refer to mean quantities of low- 
cycle years, and not to extreme minimums. The seasons of 
minimum flow, which are also, usually, the seasons of 
maximum evaporation from the storage reservoirs and of 
maximum domestic consumption, are in the calculations 
supposed to be tided over by a surplus of storage provided 
in addition to the mean storage required for the series of 
low-cycle years. The storage should therefore be in excess 
of the mean deficiency as above computed at least twenty- 
five per cent., or should equal at least fifteen per cent, of the 
mean annual rainfall. 

If the storage is less than fifteen per cent., the safe 
available supply is liable to be less than the calculations 
given. 

If the area of the storage reservoir is greater per square 
mile of watershed than assumed above, the loss by evapo¬ 
ration from the water surface will be proportionately in¬ 
creased, and must be compensated for by increased storage. 

77. Utilization of Flood Flows. —The calculations 
as above assume that fifty per cent, of the annual rainfall 
is the available annual flow in the stream. The remaining- 
fifty per cent, is assumed to be lost through the various 
processes of nature and by floods. If the storage is still 
further increased, an additional portion of the flood flow 
can be utilized, and sometimes fifty per cent, or even sixty 


INFLUENCE OF STORAGE. 


99 


per cent, of the annual rainfall utilized for domestic con¬ 
sumption, or made applicable at the outlet of the reservoir 
for power. Hence, when it is desired to utilize the greatest 
possible portion of the flow, the storage should equal twenty 
or twenty-five per cent, of the mean annual rainfall. 

78. Qualification of Deduced Ratios. —The ratios 
of flow, evaporation, and consumption, as above used in 
the calculations, are not assumed to be universally appli¬ 
cable, but are taken as safe general average ratios for the 
Atlantic Coast and Middle States. The winter consump¬ 
tion will be less in the lower Middle and Southern States, 
and also in very efficiently managed works of Northern 
States; but the summer consumption tends to be greater in 
the lower Middle and Southern States, where the evapora¬ 
tion and rainfall are greater also. 

The results upon the Pacific slope can scarcely be gen¬ 
eralized to any profit, since within a few hundred miles it 
presents extremes, from rainless desert to the maximum 
rainfall of the continent, and from vaporless atmosphere to 
constant excessive humidity. 

79. Influence of Storage upon a Continuous 
Supply. —A safe general estimate of the maximum contin¬ 
uous supply of water to be obtained from forty inches of 
annual rain upon one square mile of watershed, provided 
the storage equals at least fifteen per cent, of the rainfall, 
gives 7 cubic feet (= 52.36 gals.) per capita daily, to from 
13000 to 15000 persons, dependent upon the amount of 
available storage of winter and flood flows; or say, three- 
quarters of a million gallons of water daily. 

The same area and rain, with but one month’s deficiency 
storage, can be safely counted upon to supply but about 
3,000 persons with an equal daily consumption, or 157,000 
gallons of water daily. From the same area and rain, with 


100 


SUPPLYING CAPACITY OF WATERSHEDS. 


no storage , a fiasliy stream may fail to supply 1,000 persons 
to the full average demand in seasons of severe drought. 

Hence the importance of the storage factor in the calcu¬ 
lation. 

The above estimates are based upon mean rainfalls of 
low-cycle (§ 47) years; therefore the results may be ex¬ 
pected to be twenty per cent, greater in years of general 
average rainfall. 

80. Artificial Gathering Areas. —When resort is 
necessarily had to impervious artificial collecting areas for 
a domestic water supply, as when dwellings are located 
upon vegetable moulds or low marsh areas, bituminous 
rock surfaces, limestone surfaces, or, as in Venice, where 
the sheltering roofs are the gathering areas of the house¬ 
holds, the proportion of the rainfall that may be run into 
cisterns is very large. If such cisterns are of sufficient 
capacity and their waters protected from evaporation, eighty 
per cent, of the rainfall upon the gathering areas may thus 
be made available, though special provisions for its clarifi¬ 
cation will be indispensable. 

In such case, a roof area equivalent to 25 feet by 100 
feet might furnish from a forty-inch rainfall a continuous 
supply of 3 cubic feet (— 22.44 gallons) per day to six per¬ 
sons, which would be abundant for the household uses for 
that number of persons. 

81. Recapitulation of Rainfall Ratios. —Recapitu¬ 
lating, in the form of general average annual ratios, relating 
to the mean rainfall upon undulating crystalline or diluvial 
surface strata, as unity, we have : 


Ratio of mean annual rainfall. i.oo 

Ratio of mean rainfall of lowest three-year cycles. 80 

Ratio of minimum annual rainfall. 70 

Ratio of mean annual flow in stream (of the given year’s rain). 60 






RAINFALL RATIOS. 


101 


Ratio of mean summer flow in stream (of the given year’s rain).25 

Ratio of low summer flow in stream “ “ “ 05 

Ratio of annual available flow in stream “ “ 50 

Ratio of storage necessary to make available 50 per cent, of annual rain. .15 


Ratio of general evaporation from earths, and consumption by the pro¬ 
cesses of vegetation. 

Ratio of percolation through the earth (included also in the flow of 


streams).25 

Ratio of mean rainfall collectible upon impervious artificial or primary 

rock surfaces.80 


The monthly ratios of these annual ratios are to he taken 
in ordinary calculations of water supplies, and each annual 
ratio to he subjected to the proper modification adapting it 
to a special local application. 


TABLE No. 30 . 

Ratios of Monthly Rain, Flow, Evaporation, and Consumption. 



g 

vi 

> 

X1 
<u 

Mar. 

u 

Cu 

< 

May. 

June. 

j>> 

G 

Aug. 

Sept. 

Oct. 

i 

Nov. 

d 

0 

Q 

Ratios of average monthly rain. 

•75 

•83 

.90 

I . IO 

1.30 

1.08 

1.12 

1.20 

I .OO 

•95 

•93 

.84 

Ratios ot av. monthly flow of streams. 

1.65 

1.50 

1.65 

i -45 

•85 

•75 

•35 

• 2 5 

• 3 ° 

•45 

1.20 

1.60 

Ratios of av. monthly evap. from water 
Ratios of average monthly consump- 

• 3 ° 

•35 

• 5 ° 

. 80 

i -45 

1.70 

1.85 

2.00 

i -45 

•75 

•50 

•35 

tion of water. 

105 

I . IO 

.90 

•85 

.90 

I .OO 

1.20 

125 

1.05 

.90 

•85 

•95 


TABLE No. 3 O a . 

Example of an Estimate of Collectable Rainfall.* 


j Assumed annual rainfall 40 in. | 
j Average available monthly flow f 
1.667 in, 

G 

cS 

jd 

<u 

'r 

March. 

April. 

May. 

June. 

1 July. 

b£ 

3 

c 

Sept. 

4-T 

u 

0 

O 

fc 

d 

<V 

Q 

Total. 

Ratio of monthly mean available flow 

1.65 

1.50 

1.65 

i -45 

.85 

•75 

•35 

• 25 

•30 

•45 

1.20 

1.60 

12.00 

Equivalent inches of monthly avail- 







.58 





2.67 


able flow. 

2-75 

2.50 

2-75 

2.42 

1.42 

1-25 

• 4 1 

•50 

75 

2.00 

20.00 

Eight-tenths of do. 

2.20 

2.00 

2.20 

1 -93 

i -*3 

I .OO 

•47 

•33 

.40 

.60 

1.60 

2.13 

16.00 

Inches of rain monthly to satisfy 



• 56 

•56 






•56 


•56 

6.25 

riparian rights. 

Inches of rain collectable monthly, 

•56 

.56 

•56 

•56 

■47 

•33 

.40 

• 56 



1.64 











for storage. 

1.64 

1.44 

1 -37 

•57 

•44 

.OO 

.OO 

.OO 

.04 

1.04 

1 -57 

9-75 


The inches of rainfall flowing monthly, here assigned as a riparian right, are found by 
taking the mean of flows from June to October inclusive, thus: 

1.00 ~47 d~ -33 ~h 4 ° ~b -6o inches _ ^ j nc j ies 0 f ra j n _ 

5 months 

This allows to riparian rights the entire low water flow of summer, and allows for losses 
of rainfall approximately as follows: Loss by evaporation and absorption, 12 in.; loss by 
floods, 8 in.; reduced flow in dry seasons, 4 in.; remaining available flow, 16 in. 

* Relating to the Adirondack water shed of Hudson River. From u Report on a Water 
Supply for New York and other Cities of the Hudson Valley, by J. T. Fanning. N. Y., 1881. 








































































CII APT EE VII. 


SPRINGS AND WELLS. 

82. Subterranean Waters.—A portion of the rain, 
perhaps one-fourth part of the whole, distilled upon the 
surface of the earth, penetrates its soils, the interstices of 
the porous strata, the crevices of the rocks, and is gathered 
in the hidden recesses. These subterranean reservoirs were 
tilled in the unexplored past, and their flow continues in 
the present as they are replenished by new rainfalls. 

83. Their Source the Atmosphere. —We find no 
reason to suppose that Nature duplicates her laboratory of 
the atmosphere in the hidden recesses of the earth, from 
whence to decant the sparkling springs that issue along the 
valleys. On the other hand, we are often able to trace the 
course of the waters from the storm-clouds, into and through 
the earth until they issue again as plashing fountains and 
flow down to the ocean. 

The clouds are the immediate and only source of supply 
to the subterranean watercourses, as they are to the sur¬ 
face streams we have just passed in review. 

The subterranean supplies are subject indirectly to at¬ 
mospheric phenomena, temperatures of the seasons, surface 
evaporations, varying rainfalls, physical features of the 
surface, and porosity of the soils. Especially are the shal¬ 
low wells and springs sensitiyely subject to these influences. 

84. Porosity of Earths and Rocks. —Respecting the 
porosity and absorptive qualities of different earths, it may 
be observed that clean silicious sand, when thrown loosely 
together, has voids between its particles equal to nearly 


Fig. 131 



INTERCEPTING WELL, PROSPECT PARK, BROOKLYN. 




























































































































































































































































































































































































































































































































































































































































































































































































































THEIR SOURCE THE ATMOSPHERE. 


103 


one-tliird its volume of cubical measure ; that is, if a tank 
of one cubic yard capacity is tilled with quartzoid sand, 
then from tliirty-to thirty-five per cent, of a cubic yard of 
water can be poured into the tank with the sand without 
overflowing. 

Gravel, consisting of small water-worn stones or pebbles, 
intermixed with grains of sand, has ordinarily twenty to 
twenty-five per cent, of voids. 

Marl, consisting of limestone grains, clays, and silicious 
sands, has from ten to twenty per cent, of voids, according 
to the proportions and thoroughness of admixture of its 
constituents. 

Pure clays have innumerable interstices, not easily 
measured, but capable of absorbing, after thorough drying, 
from eight to fifteen per cent, of an equal volume of water. 

The water contained in clays is so fully subject to laws 
of molecular attraction,, owing to the minuteness of the 
individual interstices, that great pressure is required to give 
it appreciable flow. 

Water flows with some degree of freedom through sand¬ 
stones, limestones, and chalks, according to their textures, 
and they are capable of absorbing from ten to twenty per 
cent, of their equal volumes of w r ater. 

The primary and secondary formations, according to 
geological classification, as for instance, granites, serpen¬ 
tines, trappeans, gneisses, mica-slates, and argillaceous 
schists, are classed as impervious rocks, as are, usually, 
the several strata of pure clays that have been subjected to 
great superincumbent weight. 

The crevices in the impervious rocks, resulting from 
rupture, may, however, gather and lead away, as natural t 
drains, large volumes of the water of percolation. 

The free flow of the percolating water toward wells or 


104 


SPRINGS AND WELLS. 


spring, is limited and controlled, not only by the porosity 
of the strata which it enters, but also by their inclination, 
curvature, and continuous extent, and by the impervious¬ 
ness of the underlying stratum, or plutonic rock. 

85. Percolations in the Upper Strata.— Shallow 
well and spring supplies are, usually, yields of water from 
the drift formation alone. Their temperatures may be va¬ 
riable, rising and falling gradually with the mean tempera¬ 
tures of the surface soils in the circuits of the seasons, and 
they may not be wholly freed from the influence of the 
decomposed organic surface soils. Their flow T is abundant 
when evaporation upon the surface is light, though slack¬ 
ened when the surface is sealed by frost. 

A variable spring, and it is the stream at its issue that 
we term a spring, indicates, usually, a flow from a shallow, 
porous surface stratum, say, not exceeding 50 feet in depth, 
though occasionally its variableness is due to peculiar 
causes, as the melting of glaciers in elevated regions, and 
atmospheric pressure upon sources of intermittent springs. 

Porous strata of one hundred feet in depth or more give 
comparatively uniform flow and temperature to springs. 

8G. The Courses of Percolation—Gravitation tends 
to draw the particles of water that enter the earth directly 
toward the center of the earth, and they percolate in that 
direction until they meet an impervious strata, as clay, 
when they are forced to change their direction and follow 
along the impervious surface toward an outlet in a valley, 
and possibly to find an exit beneath a lake or the ocean. 

When the underlying impervious strata has considerable 
average depth, it may have been unevenly deposited in 
consequence of eddies in the depositing stream, or crowded 
into ridges by floating icebergs, or it may have been worn 
into valleys by flowing water. Subsequent deposits of 


SUBTERRANEAN RESERVOIRS. 


105 


sand and gravel would tend to till up tlie concavities and 
to even the new surface, hiding the irregularities of the 
lower strata surface. 

The irregularities of the impervious surface would not 
be concealed from the percolating waters, and their flow 
would obey the rigid laws of gravitation as unswervingly 
as do the showers upon the surface, that gather in the chan¬ 
nels of the rocky hills. 

Springs will appear where such subterranean channels 
intercept the surface valleys. The magnitude of a spring 
will be a measure of the magnitude of its subterranean 
gathering valley. 

87. Deep Percolations.—The deep flow supplies of 
wells and springs are derived, usually, from the older 
porous stratifications lying below the drift and recent cla 3 ^s. 
The stratified rocks yielding such supplies have in most 
instances been disturbed since their original depositions, 
and they are found inclined, bent, or contorted, and some¬ 
times rent asunder with many fissures, and often intercepted 
by dykes, 

88. Subterranean Reservoirs.—Subterranean basins 
store up the waters of the great rain percolations and 
deliver them to the springs or wells in constant flow, as 
surface lakes gather the floods and feed the streams with 
even, continuous delivery. A concave dip of a porous 
stratum lying between two impervious strata presents favor¬ 
able conditions for an “artesian” well, especially if the 
porous stratum reaches the surface in a broad, concentric 
plane of great circumference, around the dip, forming an 
extensive gathering area. 

Waters are sometimes gathered through inclined strata 
from very distant watersheds, and sometimes their course 


106 


SPRINGS AND WELLS. 


leads under considerable bills of more recent deposit tlian 
the stratum in which the water is flowing. 

The chalks and limestones do not admit of free percola¬ 
tion, and are unreliable as conveyers of water from distant 
gathering surfaces, since their numerous fissures, through 
which the water takes its course, are neither continuous nor 
uniform in direction. 

89. The Uncertainties of Subterranean Searches. 

—The conditions of the abundant saturation and scanty 
saturation of the strata, and their abilities to supply water 
continuously, are very varied, and may change from the 
first to the second, and even alternate, with no surface indi¬ 
cations of such result; and the subterranean flow may, in 
many localities, be in directions entirely at variance with 
the surface slopes and flow. 

Predictions of an ample supply of water from a given 
subterranean source are always extremely hazardous, until 
a thorough knowledge is obtained of the geological posi¬ 
tions, thickness, porosity, dip, and soundness of the strata, 
over all the extent that can have influence upon the flow at 
the proposed shaft. 

Experience demonstrates that water may be obtained in 
liberal quantity at one point in a stratum, while a few T rods 
distant no water is obtainable in the same stratum, an 
intervening “fault” or crevice having intercepted the flow 
and led it in another direction. Sometimes, by the exten¬ 
sion of a heading from a shaft in a water-bearing stratum, 
to increase an existing supply, a fault is pierced and the 
existing supply led off into a new channel. 

90. Renowned Application of Geological Science. 
—Arago’s prediction of a store of potable water in the deep¬ 
dipping greensand stratum beneath the city of Paris, was 
one of the most brilliant applications of geological science 


INFLUENCE OF WELLS UPON EACH OTHER. 


107 


to useful purposes. He felt keenly that a multitude of Ids 
fellow-citizens were suffering a general physical deteriora¬ 
tion for want of wholesome water, for which the splendors 
of the magnificent capital were no antidote. With a fore¬ 
sight and energy, such as displays that kind of genius that 
Cicero believed to be “in some degree inspired,” he pre¬ 
vailed upon the public Minister to inaugurate, in the year 
1833, that notable deep subterranean exploration at Gre- 
nelle. By his eloquent persuasions he maintained and 
defended the enterprise, notwithstanding the eight years of 
labor to successful issue were beset with discouragements, 
and all manner of sarcasms were showered upon the pro¬ 
moters. In February, 1841, the augur, cutting an eight- 
inch bore, reached a depth of 1806 feet 9 inches, when it 
suddenly fell eighteen inches, and a whizzing sound an¬ 
nounced that a stream of water was rising, and the well 
soon overflowed. 

91. Conditions of Overflowing’ Wells. — An over¬ 
flow results only when the surface that supplies the water¬ 
bearing stratum is at an elevation superior to the surface of 
the ground where the well is located, and the water-bearing 
stratum is confined between impervious strata. In such 
case, the hydrostatic pressure from the higher source forces 
the water up to the mouth of the bore. 

02. Influence of Wells upon Each Other.—The 
success of wells, penetrating deep into large subterranean 
basins, upon their first completion, has usually led to their 
duplication at other points within the same basin, and the 
flow of the first has often been materially checked upon the 
commencement of flow in the second, and both again upon 
the commencement of flow in a third, though neither was 
within one mile of either of the others. The flow of the 
famous well at Grenelle was seriously checked by the open- 


108 


SPRINGS AND WELLS. 


ing of another well at more than 3000 yards, or nearly two 
miles distant. 

The successful sinking of deep wells in Europe began at 
Artois, in France, in the year 1126. The name “Artesian,” 
from the name of the province of Artois, has been familiarly 
associated with such wells from that date, notwithstanding 
similar works were executed among the older nations many 
years earlier. Since the success at Artois, this method has 
been adopted in many towns of France, England, and Ger¬ 
many, where the geological structure admitted of success. 
The French engineers have recently sunk nearly one hun¬ 
dred successful wells in the great Desert of Sahara; and 
Algeria and Northern Africa are beginning to bloom in 
waste places in consequence of being watered by the pre¬ 
cious liquid sought in the depths of the earth. 

93. American Artesian Wells.—Not less than 21 
yielding wells have been sunk in Chicago varying in depth 
from 1200 to 1640 feet, the most successful of which is five 
and one half inches diameter at the bottom, yielding about 
900,000 gallons of water per 24 hours. The usual depth of 
the Chicago wells is reported to be from 1200 to 1300 feet, 
and the average cost of a five-and-a-half-inch well $6000, and 
for a four-and-a-lialf-inch well $5000, for depth of 1200 feet. 

A well for the Insane Asylum at St. Louis has reached 
a depth of 3850 feet, or 3000 feet below the level of the sea. 

Along the line of the Union Pacific Railroad, water is 
obtained at certain points by means of Artesian wells, for 
supplying the necessities of the road. 

A few Artesian wells have been sunk in Boston, but the 
water obtained has rarely been of satisfactory quality for 
domestic purposes. 

94. Watersheds of Wells.—The watershed of a deep 
subterranean supply is not so readily distinguishable as is 


WATERSHEDS OF WELLS. 


109 


that of a surface stream, that usually has its limit upon the 
crown of the ridge sweeping around its upper area. 

The subterranean watershed may possibly lie in part 
beyond the crowning ridge, where its form is usually that 
of a concentric belt, of varying width and of varying sur¬ 
face inclination. A careful examination of the position, 
nature, and dip of the strata only, can lead to an accurate 
trace of its outlines. 

The granular structure of the water-bearing stratum, as 
a vehicle for the transmission of the percolating water, is to 
be most carefully studied ; the existence of faults that may 
divert the flow of percolation are to be diligently sought 
for; and the point of lowest dip in a concave subterranean 
basin or the lowest channel line of a valley-like subterra¬ 
nean formation, is to be determined with care. 

A depressed subterranean water basin, when first dis¬ 
covered, is invariably full to its lip or point of overflow. 
Its extent may be comparatively large, and its watershed 
comparatively small, yet it will be full, and many centuries 
may have elapsed since it w T as moulded and first began to 
store the precious showers of heaven. A few drops accu¬ 
mulated from each of the thousand showers of each decade, 
may have filled it to its brim many generations since ; yet 
this is no evidence that it is inexhaustible. If the perennial 
draught exceeds the amount the storms give to its replen¬ 
ishment, it will surely cease, in time, to yield the surplus. 

Coarse sands will, when fully exposed, absorb the 
greater portion of the showers, but such sands are usually 
covered with more or less vegetable soil, except in regions 
where showers seldom fall. 

Fissured limestones and chalks will also absorb a large 
portion of the storms, if exposed, but they are rarely en¬ 
tirely uncovered except upon steep cliff faces, where there 


110 


SPRINGS AND WELLS. 


is little opportunity for tlie storms that drive against them 
to secure lodgement. 

95. Evaporation from Soils.—Vegetable and surface 
soils that do not permit free percolation of their waters 
downward to a depth of at least three feet, lose a part of 
it by evaporation. On the other hand, evaporation opens 
the surface pores of close soils, so that they receive a por¬ 
tion of the rain freely. 

96. Supplying- Capacity of Wells and Springs.— 

Percolation in ordinary soils takes place in greatest part 
in the early spring and late autumn months, and to a lim¬ 
ited extent in the hot months. In cold climates it ceases 
almost entirely when the earth is encased with frost. 

Permanent subterranean well or spring supplies receive 
rarely more than a very small share of their yearly replen¬ 
ishment between each May and October, their continuous 
flow being dependent upon adequate subterranean storage. 

Such storage may be due to collections in broad basins, 
to collections in numerous fissures in the rocks, or to very 
gradual flow long distances through a porous stratum where 
it is subject to all the limiting effects of retardation included 
under the general term, friction. 

In the latter case a great volume of earth is saturated, 
and a great volume of water is in course of transmission, 
and the flow continues but slightly diminished until after 
a drought upon the surface is over and the parched surface 
soils are again saturated and filling the interstices of perco¬ 
lation anew. 

For an approximate computation of the volume of per¬ 
colation into one square mile of porous gathering area, 
covered with the ordinary superficial layer of vegetable soil, 
and under usual favorable conditions generally, let us 
assume that the mean annual rainfall is 40 inches in depth, 


SUPPLYING CAPACITY OF WELLS AND SPRINGS. Ill 


and that in the seasons of droughts, or the so-called dry 
years, 60 per cent, of the mean monthly percolation will 
take place. 

TABLE No. 3 1 . 

Percolation of Rain into One Square Mile of Porous Soil. 


Assumed Mean Annual Rain 40 Inches Depth. 



d 

0$ 

> 

Feb. 

M ar. 

Apr. 

May. 

June. 

July. 

Aug. 

Sept. 

•J 

0 

0 

Nov. 

Dec. 

Total. | 

Ratios of r V of mean 














annual rain. 


•737 

.796 

I.O7O 

.814 

1.462 

.964 

1.077 

1.251 

1.015 

1.076 

.OQ7 

.801 






Inches of rain each 













month. 


2-457 

2 653 

3-567 

2.713 

4-873 

3-2x3 

3-590 

4.170 

3-383 

3-587 

3.123 

2.67O 

40 



Ratios of Percolation.. 
Mean inches of Rain 

•50 

.40 

•45 

•15 

•055 

.02 

.OI 

•005 

.OI 

.20 

•50 

•70 


Percolating. 


1.228 

1.061 

1.605 

•407 

.268 

.064 

.036 

.021 

•034 

.717 

1.561 

1.869 





Sixty per cent, of do. in 





,l6l 








dry years. 


•737 

•637 

•9 6 3 

•244 

.038 

.022 

.013 

.020 

•43° 

•937 

X.121 


Volume of Perco- 


00 

Os 

00 

01 

■T 

VO 

IT) 

CO 

N 

00 

0 

w 

01 

0 

VO 

VO 

00 

CO 

O 


lation in dry- 

* 

of 

CO 

6s 

of 

00 

VO* 

O r 

4- 

01 

ocf 

M 

01 

0 

vcT 

O 

06 

TO 

vcf 

CO 


years. 


M 

t ^ 

•T 

M 

co 

VO 


00 

XT) 

CO 

■T 

Os 


vg 

01 



IS 

M 

of 








of 


No. of persons it would 














supply at 5 cu. 

ft. 














each daily. 


11,046 

10,570 

x 4,434 

3i779 

2,413 

588 

33° 

195 

310 

6,445 

14.512 

16.802 



From springs , with the aid of capacious storage reser¬ 
voirs, it might be possible to utilize fifty per cent, of the 
above volume of percolation. From wells , it would rarely 
be possible to utilize more than from ten to twenty per cent, 
of the volume. 

Fifty per cent, of the above total estimated volume of 
percolation would be equivalent to a continuous supply of 
5 cubic feet per day each, to 3391 persons, or 126,823 gal¬ 
lons per diem ; and ten per cent, of the same volume would 
be equivalent to a like supply (37.4 gals, daily) to 678 
persons, or 25,357 gallons per diem. 

Wells sunk in a great sandy plain bordering upon the 
ocean, or bordered by a dyke of impervious material, would 
give greater and more favorable results, for in such case the 
conditions of subterranean storage would be most favorable, 
but such are exceptional cases. 








































CHAPTER VIII. 


IMPURITIES OF WATER. 

97. The Composition of Water.—If a quantity of 
pure water is separated, chemically, the constituent parts 
will be two in number, one of which weighing one-nintli as 
much as the whole will be hydrogen, and the other part 
oxygen ; or if the parts of the same quantity be designated 
by volume, two parts will be hydrogen and one part oxygen. 

These two gases, in just these proportions, had entered 
simultaneously into a wondrous union, the mystery of 
which the human mind has not yet fathomed. In fact, 
many years of intense intellectual labor of such profound 
investigators as Cavendish, Lemery, Lavoisier, Volta, Hum¬ 
boldt, Gay Lussac, and Dumas were consumed before the 
discovery of the proportions of the two gases that were 
capable of entering into this mystic union. 

98. Solutions in Water.—If two volumes of oxygen 
are presented to two volumes of hydrogen, one only of the 
oxygen volumes will be capable of entering the union, and 
the other can only be diffused through the compound, water. 

When alcohol is poured into water it does not become 
a part of the water, but is diffused through it. 

This we are assured of, since by an ingenious operation 
we are able to syphon the alcohol out of the water by a 
method entirely mechanical. If 'we put some sugar, or 
alum, or carbonate of soda into water, the water will cause 
the crystals to separate and be diffused throughout the 
liquid, but they will not be a part of the water. The water 








* 



HORIZONTAL TURBINES AND PUMPS. To r»ce P . 1J2, 

Wju-imantic Water Works, Conn. 





































































































































































































































































































































PROPERTIES OF WATER. 


113 


might be evaporated away, when the sugar, or alum, or 
soda would have returned to its crystalline state. In these 
cases, the surplus hydrogen, the alcohol, and the constitu¬ 
ents of the crystalline ingredient are diffused through the 
water as impurities. 

If in a running brook a lump of rock salt is placed, the 
current will flow around it, and the water attack it, and will 
dissolve some of its particles, and they will be diffused 
through the whole stream below. A like effect results when 
a streamlet flows across a vein of salt in the earth. In like 
manner, if water meets in its passage over or through the 
earth, magnesium, potassium, aluminium, iron, arsenic, or 
other of the metallic elements, it dissolves a part of them, 
and they are diffused through it as impurities. In like 
manner, if water in its passage through the air, as in 
showers, meets nitrogen, carbonic acid, or other gases, 
they are absorbed and are diffused through it as impurities. 

99. Properties of Water.—Both oxygen gas and 
hydrogen gas, when pure, are colorless, and have neither 
taste nor smell. Water, a result of their combination, when 
pure, is transparent, tasteless, inodorous, and colorless, 
except when seen in considerable depth. 

The solvent powers of water exceed those of any other 
liquid known to chemists, and it has an extensive range of 
affinities. This is why it is almost impossible to secure 
water free from impurities, and why almost every substance 
in nature enters into solution in water. There is a property 
in writer capable of overcoming the cohesive force of the 
particles of matter in a great variety of solids and liquids, 
and of overcoming the repulsive force in gases. The par¬ 
ticles are then distributed by molecular activities, and the 
result is termed solution. 

Some substances resist this action of water with a large 


114 


IMPURITIES OF WATER, 


degree of success, though not perfectly, as rock crystals, 
various spars and gems, and vitrified mineral substances. 

100. Physiological Effects of the Impurities of 
Water. —When we remember that seventy-five per cent, of 
our whole body is constituted of the elements of water, that 
not less than ninety-five per cent, of our healthy blood, and 
not less than eighty per cent, of our food is also of water, 
we readily acknowledge the important part it plays in our 
very existence. 

Water is directly and indirectly the agency that dissolves 
our foods and separates them, and the vehicle by which the 
appropriate parts are transmitted in the body, one part to 
the skin, one to the finger-nail, one to the eye-lash, to the 
bones phosphate of lime, to the flesh casein, to the blood 
albumen, to the muscles fibrin, etc. When the stomach is 
in healthy condition, nature calls for water in just the 
required amount through the sensation, thirst. Good 
water then regulates the digestive fluids, and repairs the 
losses from the watery part of the blood by evaporation 
and the actions of the secreting and exhaling organs. 
Through the agency of perspiration it assists in the regula¬ 
tion of heat in the body; it cools a feverish blood ; and it 
allays a parching thirst more effectually than can any fer¬ 
mented liquor. Water is not less essential for the regula¬ 
tion of all the organs of motion, of sight, of hearing, and 
of reason, than is the invigorating atmosphere that ever sur¬ 
rounds us, to the maintenance of the beating of the heart. 

If from a simple plant that may be torn asunder and yet 
revive, or a hydra that may be cut across the stomach or 
turned wrong side out and still retain its animal functions, 
the water is quite dried away, if but for an instant, man, 
with his wonderful constructive ability, and reason almost 


MINERAL IMPURITIES. 


115 


divine, cannot restore that water so as to return the activity 
of life and the power of reproduction. 

The human stomach and constitution become toughened 
in time so as to resist obstinately the pernicious effects of 
certain of the milder noxious impurities in water, but such 
impurities have effect inevitably, though sometimes so grad¬ 
ually that their real influence is not recognized until the 
whole constitution has suffered, or perhaps until vigor is 
almost destroyed. 

Note the effect of a few catnip leaves thrown into drink¬ 
ing water, which will act through the water upon the nerves ; 
or an excess of magnesia in the water will neutralize the free 
acids in the stomach, or lead in the water w T ill act upon the 
gums and certain joints in the limbs, or alcohol will act 
upon the brain; and so various vegetable and mineral solu¬ 
tions act upon various parts of the body. 

It would be fortunate if the pernicious impurities in 
water affected only matured constitutions, but they act with 
most deplorable effect in the helplessness of youth and even 
before the youth has reached the light. These impurities 
silently but steadily derange the digestive organs, destroy 
the healthy tone of the system, and bring the living tissues 
into a condition peculiarly predisposed to attack by malig¬ 
nant disease. 

101. Mineral Impurities. —The purest natural waters 
found upon the earth are usually those that have come 
down in natural streams from granite hills ; but if a thou¬ 
sand of such streams are carefully analyzed, not one of them 
will be found to be wholly free from some admixture. This 
indicates that in the economy of nature it has not been 
ordained to be best for man to receive water in the state 
chemically called pure. A United States gallon of water 
weighs sixty thousand grains nearly. Such waters as phy- 


116 


IMPURITIES OF WATER. 


sicians usually pronounce good potable waters have from 
one to eight of these grains weight, in each gallon, of certain 
impurities diffused through them. These impurities are 
usually marshalled into two general classes, the one derived 
more immediately from minerals, the other derived directly 
or indirectly from living organisms. The first are termed 
mineral impurities, and the other organic impurities. 

The mineral impurities may be resolved by the chemist 
into their original elementary forms, and they are usually 
found to be one or more of the most generally distributed 
metallic elements, as calcium, magnesium, iron, sodium, 
potassium, etc. If as extracted they are found united with 
carbonic acid, they are in this condition termed carbonates ; 
if with sulphuric acid, sulphates; if with silicic acid, sili¬ 
cates ; if with nitric acid, nitrates ; if with phosphoric acid, 
phosphates , etc.; if one of these elements is formed into a 
compound with chlorine, it is termed a chloride; if with 
bromine, it is termed a bromide , etc. A few metallic ele¬ 
ments may thus be reported, in different analyses, under a 
great variety of conditions. 

102 . Organic Impurities, —There are a few elements 
that united form organic matter, as carbon, oxygen, hydro¬ 
gen, nitrogen, sulphur, phosphorus, potassium, calcium, 
sodium, silicon, manganese, magnesium, chlorine, iron, and 
fluorine. Certain of these enter into each organized body, 
and their mode of union therein yet remains sealed in mys¬ 
tery. In the results we recognize all animated creations, 
from the lowest order of plants to the most perfect quadru¬ 
peds and the human species. All organic bodies may, 
however, upon the extinction of their vitality, be decom¬ 
posed by heat in the presence of oxygen, and by fermenta¬ 
tion and putrefaction. 

The metallic elements are, in the impurities of good 


ANALYSES OF POTABLE WATERS. 


117 


potable waters, usually much in excess of the organic ele¬ 
ments, but the contained nitrogenized organic impurities 
indicate contaminations likely to be much more harmful to 
the constitution, and especially if they are products of ani¬ 
mal decompositions. 

103. Tables of Analyses of Potable Waters. —We 
will quote here several analyses of running and quiet waters 
that have been used, or were proposed for public water 
supplies, indicating such impurities as are most ordinarily 
detected by chemists in water. For condensation and for 
convenience of comparison they are arranged in tabular 
form. 


TABLE No. 32 . 

Analysis of various Lake, Spring, and Well Waters. 



Jamaica Pond, near 
Brooklyn, L. 1 . 

Flax Pond, near 

Lynn, Mass. 

Sluice Pond, near 

Lynn, Mass. 

Breeds Pond, near 

Lynn, Mass. 

Reeds’ Lake, near 
Grand Rapids, Mich. 

Lake Konomac, near 
New London, Conn. 

Loch Katrine, near 
Glasgow, Scotland. 

b 

C 

Sc 

£ 6 

.£ a, 

o 3 

Ml) 

Well at Highgate, 
England. 

Artesian Well, at 

Hatton, ,England. 

Artesian Well, at 
Colney Hatch, England. 

Carbonate of Lime. 

1.092 

.700 

.400 

.600 

4-65 

.096 


12.583 


1.768 

5.420 

“ Magnesia. 

.408 

.692 

.320 

.612 

113 

.... 

.216 

II.658 

.... 

•734 

I.IOI 

“ Soda. 

.... 

.... 

... 


.... 



12.677 

5.921 

Protocarbonate of Iron.. 










4.00 

Chloride of Sodium. 

.244 

.612 

.408 

•504 

.... 

2.18 

.... 

9-556 

8.032 

7-745 


“ Magnesia... 

.328 

, . . , 



trace 

.... 

.... 


3-553 

“ Calcium. ... 

.120 

... 

.... 


.... 

.... 

.144 

.... 

4 - 93 ° 

.... 

“ Potassium... 


. . . 



1.62 







Alkaline Chlorides. 

.... 

.... 

.... 



.... 

•433 





Sulphate of Lime. 

.120 

.300 

• 3 °° 

.270 

. . . • 

1.29 

.381 

12.775 

. . . . 

• • • • 

3-798 

“ Magnesia... 

.288 

.... 

.... 

.050 

.... 

... 


, . . . 

, . . . 

.... 


“ Potash. 

.... 

.064 

.O7O 

.... 

.... 

. . . . 


. . . . 

14.217 

trace 

2.160 

“ Potassa. 

.... 



.... 


5.662 

.... 


“ Soda. 

Phosphate of Lime. 

Nitrate of Lime. 


.080 

.086 

. . CO 

. . 00 
0 

trace 

• • • • 


8.776 

7-935 

33-457 

8 - 7 i 9 

trace 

4.811 

trace 

“ Magnesia. 

.... 

.... 

. . . . 

.... 

.... 

.... 


.... 

14.23 1 

.... 

.... 

Oxide of Iron. 

.044 

O 

00 

trace 

.096 

.85 

.035 trace 

.... 

.... 

.... 

.... 

Ammonia. 


. . . . 

. . . . 


.... 

. . . , 

.... 


.... 

... 

Silica. . 

• • • • 

.156 

.144 

.120 

•75 

2-43 

.170 

.200 

•747 

.042 

•559 

Organic Matter. 

.008 

2.208 

1-344 

2.184 

8-75 

1.80 

.900 

3-419 

.... 

.... 

Total Solids. 

2.652 

5.652 

3.072 

5 - 3 l6 

i 7 - 75 o 

7-831 

2.244 

64.629 

83-549 

35-685 

27-323 

Soluble Organic Matter. 


• • • • 




• • • • 





•392 

Hardness, Degrees by 
Clark’s Scale. 

.... 

.... 

.... 

.... 

.... 

• • • • 

0.80 



.... 

.... 














































































118 


IMPURITIES OF WATER. 


TABLE 

Analysis of various 


The quantities are expressed in 
grains per U. S. Gallon of 231 cubic 
inches, or 58,372^0 grains. 

Hudson River, above 
Albany, N. Y. 

Hudson River, above 
Poughkeepsie, N. Y. 

Connecticut River, 
above Holyoke, Mass. 

Connecticut River, 

above Springfield, Mass. 

Schuylkill River, above 
Philadelphia, Pa. 

Croton River, above 

Croton Dam, N. Y. 

Croton River Water in 

New York Pipes, N. Y. 

Saugus River, near 

Lynn, Mass. 

Carbonate of Lime. 


1.059 

•85 

•56 

.90 

.67 

1.56 

.60 

2.67 

1.90 

1.52 

.84 

1.812 

“ Magnesia. 



44 Soria . 


2.126 











r^hlnrirlf* of SoHinm . 

.361 

.l6l 

.108 

.676 

.72 

•49 

.402 


.480 

44 TYTafrnpsia. 


44 da 1 Hum... 





.86 

•QO 


“ Potassium. 



.070 

.090 

.146 

.83 

•75 

.156 




“ u and Sodium .... 

Sulphate of r.ime. 

.980 

.... 

.29 

’.'158 


.280 

“ Magnesia . 



“ Potash . 

.076 







.028 

“ Potassa. 

“ Soda. 

2.785 

.... 

.... 

•43 

.48 

.179 

.200 


.040 

Silicate of Potassa. 

“ Soda . 

.... 

.... 

.... 



Nitrate of Lime. 









Oxide of Iron. 


3-644 

.156 

.168 

.09 

trace 


trace 

Iron Alumina and Phosphates. 

Ammonia .... . 

.... 




Silira . 

.408 

.699 

2.201 

.132 

1.728 

•i 33 

1.680 

•30 

.62 

.46 

I. 104 
2.880 

Orsranie Matter . 

.776 

.67 




Total Solids. 

2.685 

12.699 

4.408 

6.007 

4.24 

7.719 

3.720 

6.624 

Soluble Orcranie Matter . 

Solid residue obtained on evaporation. 
Free Carbonic Acid. 

.... 

.... 

.... 

.... 

.... 

.... 

.... 

.... 

Hardness, Degree by Clarke’s Scale... 

3-35 

.... 

•43 

• 5 1 

.... 

.... 

.... 

.... 


* Notwithstanding the exceeding importance of an intelligent microscopi¬ 
cal examination of each proposed domestic water supply, in addition to the 
chemical analysis, no record of such examination is found accompanying the 
reports upon the waters herein enumerated. Lenses of the highest microscop¬ 
ical powers should he used for such purpose, and immersion lenses are required 
in many instances. 

To obtain specimens of sedimentary matters, the sample of water may first 










































































ANALYSIS OF POTABLE WATERS 


119 


No. 33 . 

River and Brook Waters.* 


Chickopee River, near 
Springfield, Mass. 

Mill River, near 
Springfield, Mass. 

1 

Grand River, above 
Grand Rapids, Mich. 

White River, in Filter 
Wells on Bank, at 
Indianapolis, Md. 

Kallkill Creek, near 
Poughkeepsie, N. Y. 

Wapinger’s Creek, near 
Poughkeepsie, N. Y. 

Lynde Brook, near 
Worcester, Mass. 

Thames River, above 
London, Eng. 

Dee River, near 
Aberdeen, Scotland. 

New River, London, 

Eng. 

Hampstead Water Co.’s 

Supplj'-, England. 

Cowley Brook, near 

Preston, Eng. 

Loud Scales, Preston, 

England. 

Dutton Brook, near 

Preston, Eng. 

•65 

1.30 

7.18 

10.02 

•51 

6.221 

•334 

13-13 

.709 

6.521 

4.128 

•575 

6.131 

1-343 

•59 

.87 

1.84 

.... 

.... 

.... 

•05 

.... 

.... 

.909 

2.944 

.238 

.966 

.217 


... 


.40 

• 3 22 

4- 2 45 

.... 

.... 

.... 

.... 

.... 

.... 

.... 

.... 

.... 

.... 


. . . 

.... 

.... 

.... 

.... 

. . . 

.... 

.... 

.147 

.242 

.152 

• 53 2 

.865 


4.70 

1.20 

trace 

.... 

1.56 

.... 

1.442 

5.662 

•938 

•550 

• 97 ° 

• • • 

.... 


.... 

.... 

.... 

.... 

.... 

. . . 

.... 

. . . 

.091 

.... 

.... 

.... 

.... 


2 -37 

.... 

.... 

•334 

.... 

.... 

.... 

.... 

.... 

• 3*7 

.... 

•75 

•°7 

OO 

CO 

.... 

.... 

.... 

.... 

.... 

.... 

.... 

1.501 

.... 

.... 

.... 

.64 

.11 


.... 

.... 

.... 

.... 


•559 

.... 

•_ 

.... 

. . . 

.... 

•13 

.260 


3.00 

.... 

.... 

.... 

2-73 

.IOI 

2.693 

.... 

•175 

.321 

.105 

• . . . 

.... 


.... 

.... 

... 

.... 

.... 


.... 

.... 

.... 

.... 

•394 

.... 

.... 


• • • • 

.... 

.... 

• • • 

.... 


.926 

1.167 

.287 

•i 33 

•i 59 

... 

• • • • 


.... 

trace 

.092 

.150 

.... 


1.242 

12.625 

.... 

.780 

.171 

.... 

.... 


. ... 

.... 

.... 


.... 


.... 


•093 

.... 


.... 

.... 


.... 

.... 

.... 

• . . 

.... 


.... 

.... 

•348 

. . • 


.... 

.... 


.... 


.... 

.... 

.... 


.017 

.058 

.... 

.... 


trace 

trace 

•72 

• • • • 

1.66 

.851 

.167 

• r 3 


.... 

.... 

.... 

.... 


• • • • 

.... 


.... 

• • • • 


.... 



trace 

trace 

.... 

• • • • 


• • • • 

.... 


• • • • 


• • • • 

• • • • 

.... 


trace 

trace 

... 

.... 


.12 

trace 

i -37 

.... 

trace 

•05 

• 2 75 

•27 


.417 

.058 

•425 

•334 

.401 

I. IO4 

3.864 

18.75 

•50 

•15 

trace 

.417 

2-37 


2.327 

i -535 

.... 

.... 

.... 

4.516 

7-339 

3 I<2 4 

20.99 

6.74 

n -459 

1.727 

20.19 

.... 

16.496 

29.678 

3 - 3*7 

1-774 

3.912 












1.167 

1.168 

•785 

.... 

.... 

. • . 

.... 

.... 

.... 

.... 

.... 

.... 

16.327 

25-527 

3 - 5°2 

9-340 

4.144 

... a 

.... 

. • . . 

.... 

.... 

.... 

.... 

.... 

.... 

6.037 

5-562 

.... 

4-633 

.... 

•30 

•63 

.... 

• • • • 

• • • • 

• • • • 

.... 

14-5 

• • • • 

* 4-9 

9.8 

1.25 

12 

1.50 


rest a day in a deep, narrow disli, and then have its clear upper water syphoned 
off. The remainder of the water may then be poured into a conical glass, such 
as, or similar to, the graduated glasses used by apothecaries, and then again 
allowed to rest until the sediment is concentrated, when the greater part of the 
clear water may be carefully syphoned off and the sediment gathered and 
transferred to a slide, where it should be protected by a thin glass cover. 













































































120 


IMPURITIES OF WATER. 


TABLE No. 34. 

Analysis of Streams in Massachusetts.* 
(Quantities in Grains per U. S. Gallon.) 





Solid Residue of 
Filtered Water. 



Free 

Ammonia. 

Albuminoid 

Ammonia. 

Inorganic. 

Organic and 

Volatile. 

Total. 

Chlorine. 

1 

Merrimac River—Mean of n ex¬ 
aminations above Lowell. 

O.OO27 

j 

O.0066 

1.38 

I .OI 

2-39 

O.08 

Merrimac River—Mean of 12 ex¬ 
aminations above Lawrence. 

.0026 

.0064 

1.41 

.98 

2-39 

. 12 

Merrimac River—Mean of n ex¬ 
aminations below Lawrence. 

.OOl8 

.0074 

i -54 

I.05 

2-59 

.11 

Blackstone River, near Quinsig- 
amund Iron Works. 

.105 

.015 

1.98 

I.98 

3-96 

•5° 

Blackstone River, just above Mill- 
bury. 

.024 

.012 

2.62 

i -75 

4-37 

•37 

Blackstone River, below Black¬ 
stone . 

.004 

.008 

1.66 

1.21 

2.87 

.21 

Charles River, at Waltham. 

•0035 

.0096 

2.26 

1.07 

3-33 

•23 

Sudbury River, above Ashland.... 

.0030 

.0107 

1.63 

2.50 

4-13 

•23 

Sudbury River, at Concord. 

.0026 

.0115 

2.22 

i- 3 i 

3-53 

. l8 

Concord River, at Concord. 

.0047 

.OI58 

1.80 

1.42 

3.22 

.20 

Concord River, at Lowell. 

.0027 

.OO97 

2.85 

i -59 

4.44 

.26 

Neponset River, at Readville. 

.0027 

.OI58 

1.40 

1.98 

3-38 

.20 

Neponset River, below Hyde Park. 

.0064 

•0175 

2.10 

1.77 

3-87 

•30 


104. Ratios of Standard Gallons. — A portion of tins 
above analyses were found with their quantities of im¬ 
purities expressed in grains per imperial gallon, a British 
standard measure containing 70,000 grains, and some of 
them expressed in parts per 100,000 parts. They have all 
been, as have those following, reduced to grains in a U. S. 
standard gallon, containing 58372.175 grains. 

The degrees of hardness are expressed by Clark’s scale, 
which refers to the imperial gallon. 


* Selected from the Fifth Annual Report of the Mass. State Board of 
Health. 









































ANALYSES OF WELL WATERS. 


121 


The other quantities may he easily reduced to equiva¬ 
lents for imperial gallons, by aid of logarithms of the quan¬ 
tities or of the ratios : 


Imperial gallon — No. of grains . 

. 70000 Logarithm, 4.845098 

U. S. gallon — No. of grains . 

• 58372.175 

<< 

4.766206 

Ratio of imp. to U. S. gallon . 

. 1.199201 

<4 

0.078892 

“ of U. S. to imperial gallon . 

. .833886 

U 

1.921108 

“ of cubic foot to one imp. gallon. 

.. 6.23210 

a 

0.794634 

n a U U U U U S 

.. 7-48052 

U 

0.873932 

“ “ one imp. gall, to one cu. ft. . 

.. .16046 

a 

1.205367 

“ “ “ U.S. “ “ “ “ . 

.. .13368 

cc 

1.126066 


The following analyses of various well waters are in a 
more condensed form: 

TABLE No. 35 . 

Analyses of Water Supplies from Domestic Wells. 

(Quantities in Grains per U. S. Gallons.) 


Wells. 


Albany, Capital Park. 

“ Lydius Street. 

“ average of several. 

Boston, Beacon Hill. 

“ Tremont Street. 

“ Long Acre. 

“ average of three. 

“ Old Artesian. 

Brookline, Mass. 

Brooklyn, L. I. 

“ average of several. 

Charlestown, Mass. 

Cape Cod. 

Detroit, Mich. > . 

Dayton, Ohio. . 

Dedham, Mass., Driven Pipe. 

“ “ Artesian. 

Fall River, Mass., average of seventeen.. 

Hartford, Conn., No. .. 

“ “ No. 2. 

“ “ No. 3. 

“ “ No. 4. 

“ “ No. 5. 


Mineral 

Matters. 

Organic 

Matters. 

Total 

Solids. 

Hardness, 1 
Clark’s 
Scale. 

• • • • 

• • • • 

65.20 




19.24 




48.69 




50.00 




26.60 




56.80 




44.46 


54-35 

I.85 

55-20 


9.89 

4.08 

13-97 


• • • • 

.... 

45-40 


• • • • 

• • • • 

48.83 


• • • • 

• • • • 

26.40 


10.01 

2.41 

12.42 


• • • • 

• • • • 

116.46 


• • • • 

* • • » 

56.50 


5.12 

1.12 

6.24 


4.08 

1.11 

5-19 


25.16 

7.00 

32.16 

12.17 



19-33 

8-39 



32.16 

13-44 



37.10 

.... 



43.60 

10.55 



69.05 

19.22 



























































122 


IMPURITIES OF WATER. 


Analyses of Water Supplies from Domestic Wells—( Continued ). 


Wells. 

Mineral 

Matters. 

Organic 

Matters. 

Total 

Solids. 

Hardness, 

Clark’s 

Scale. 

Indianapolis, Ind. 


.... 

60 OO 

• • • • 

Lowell, Mass., average of fifteen. 

.... 

• • • • 

39-33 

8.71 

London, Eng., Leadenhall Street. 

90.38 

9-59 

99-97 


“ “ St. Paul’s Churchyard. ... 

• • • • 

• • • • 

62.54 


Lambeth, “ . 

. • • • 

• • • • 

83-39 


Lvnn, Mass. 

• • • • 

• • • • 

34.08 


Manhattan, N. Y. 

.... 

• • • • 

104.00 


“ ' “ average of several. 

• • • • 

• • • • 

49.00 


New Haven, Conn., average of five. 

• • • • 

• • • 

20.32 


New York, west of Central Park. 

38.95 

4-59 

43-54 


“ average of several. 

.... 

.... 

58.00 


Newark, N. J., average of several. 

.... 

• • • • 

19.36 


Providence R. I., average of twenty-four. 

24.05 

8.82 

33-02 

10.87 

“ “ purest of “ 

7.76 

3-35 

11 . 11 

7.70 

“ “ foulest of " 

56.99 

24.12 

81.11 

22.26 

Portland, Me., average of four . 

13-35 

5.13 

18.48 


Pawtucket, R. 1 . 

29.16 

3-03 

32.19 


a a 

25.08 

3-73 

28.81 


ii ii 

18.68 

3.62 

22.30 


Paris, France, Artesian.. . 

• • • • 

• • • • 

9.86 


Rochester, N. Y., average of several . 

• • • « 

.... 

30.00 


Rye Beach, N. H . 

6.08 

2-43 

8.51 


Springfield, Mass . 

7.82 

2.03 

9-85 


<< t< 

8 .8l 

2.01 

10.82 


i 4 (( 

n -53 

1.91 

13-44 


i€ ii 

14.83 

3.08 

17.91 


Schenectady, N. Y., State Street . 

46.88 

2.33 

49.21 


Taunton, Mass . 

20.14 

2.98 

23.12 


ii ( i 

39.86 

4.09 

43-95 


Waltham, “ . 

7.68 

4.08 

11.76 


“ “ Pump . 

17.79 

7.46 

25-25 


Winchester," :. 

4.00 

2.40 

6.40 


ii ii 

8.00 

2.40 

10.40 


u a 

10.80 

2.04 

13.20 


Woburn, Mass., average of four . 

51-52 

4.60 

56.12 



105. Atmospheric Impurities. —The constant disin¬ 
tegration of mineral matters and the constant dissolutions 
of organic matters, and their disseminations in the at¬ 
mosphere, offer to falling rains ever-present sources of ad¬ 
mixture, finely comminuted till just on the verge of trans¬ 
formation into their original elements. The force of the 
winds, the movements of animals, the actions of machines, 



























































SUB-SURFACE IMPURITIES. 


123 


are every moment producing friction and rubbing off minute 
particles of rocks and woods and textile fabrics. Decaying 
organisms, breaking into fibre, are cauglit up and wafted 
and distributed hither and thither. 

The. atmosphere is thus burdened with a mass of lifeless 
particles pulverized to transparency. 

* A ray of strong light thrown through the atmosphere in 
the night, or in a dark room, reveals by reflection this sea of 
matter that vision passes through in the light of noon-day. 
These matters the mists and the showers absorb, and dis¬ 
solve in solution. 

The respirations of all animate beings, the combustions 
of all hearth-stones and furnaces, and the decaying dead 
animals and vegetables, continually evolve acid and sul¬ 
phurous gases into the atmosphere. Chief among the del¬ 
eterious gases arising from decompositions are carbonic 
acid, nitrous and nitric acids, chlorine, and ammonia. 
These are all soluble in water, and the mists and showers 
absorb them freely. Ehrenberg states that, exclusive of 
inorganic substances, he has detected three hundred and 
twenty species of organic forms in the dust of the winds. 
Hence the so-called pure waters of heaven are fouled, before 
they reach the earth, with the solids and gases of earth. 

106. Sub-surface Impurities. —The waters that flow 
over or through the crevices of the granites, gneisses, ser¬ 
pentines, trappeans, and mica slates, or the silicious sand¬ 
stones, or over the earths resulting from their disintegrations, 
are not usually impregnated with them to a harmful extent, 
they being nearly insoluble in pure water. 

The limestones and chalks often impart qualities objec¬ 
tionable in potable waters, and troublesome in the house¬ 
hold uses and in processes of art and manufacture. 

The drift formation, wherever it extends, if unpolluted 


124 


IMPURITIES OF WATER. 


by organic remains upon or in its surface soil, usually sup¬ 
plies a wholesome water. 

The presence of carbonic acid in water adds materially 
to its solvent power upon many ingredients of the soil that 
are often present in the drift, such as sulphate of lime, 
chloride of sodium, and magnesian salts, and upon organic 
matters of the surface. 

Carbonic acid in rain-water that soaks through foul sur¬ 
face soils, gives the water power to carry down to the wells 
a superabundance of impurities. 

The presence of ammonia is a quite sure indication of 
recent contamination with decaying organic matter capable 
of yielding ammonia, whether in spring, stream, or well. 
This readily oxidizes, and is thus converted into nitrous 
acid and by longer exposure into nitric acid. 

These acids combine freely with a lime base, as nitrate 
and nitrite of lime. 

Analysts attach great importance to the nature of the 
nitrates and nitrites present, as indications of the nature of 
the contaminations of the water. 

Some of the subterranean waters penetrate occasional 
strata that wholly unlit them for domestic use. A portion 
of the carboniferous rocks are composed so largely of min¬ 
eral salts that their waters partake of the nature of brine, as 
in parts of Ohio ; in the Kanawha Valley, West Virginia ; 
and in parts of New York State ; for instance, at Syracuse, 
where the manufacture of salt from sub-surface water has 
assumed great commercial importance. In other sections, 
the bituminous limestones are saturated with coal-oils, as in 
the famous oil regions of Pennsylvania. The dark waters 
from the sulphurous strata of the Niagara group of the 
Ontario geological division are frequently impregnated with 
sulphuretted hydrogen. 


HARDENING IMPURITIES. 


125 


All along the western flank of the Appalachian chain, 
from St. Albans and Saratoga on the north to the White 
Sulphur Springs on the south, the frequent mineral springs 
give evidence of the saline sub-structure of the lands, while 
like evidences have recently become conspicuous in certain 
portions of Kentucky, Arizona, New Mexico, Utah, Califor¬ 
nia, and Oregon. 

107. Deep-well Impurities. —Deep well and spring 
waters, except those from dipping sand or sandstone strata, 
are especially liable to impregnations of mineral salts. 

These impurities from deep and hidden sources, when 
present in quantities that will be harmful to the animal 
constitution, are almost invariably perceptible to the taste, 
and are rejected instinctively. 

108. Hardening* Impurities. —The solutions of salts 
of lime and magnesia are among the chief causes of the 
quality called hardness in water. Their carbonates are 
broken up by boiling, for the heat dissipates the carbonic 
acid, when the insoluble bases are deposited, and, with such 
other insoluble matters as are present, form incrustations 
such as are seen in tea-kettles and boilers where hard waters 
have been heated. The carbonates, in moderate quantities, 
are less troublesome to human constitutions than to steam 
users. The effects of the carbonates are termed temporary 
hardness. The sulphates, chlorides, and nitrates of lime 
and magnesia are not dissipated by ordinary boiling. 
Their effects are therefore termed permanent hardness. 

An imperial gallon of pure water can take up but about 
two grains of carbonate of lime, when it is said to have two 
degrees of hardness; but the presence of carbonic acid in 
the water will enable the same 70,000 grains of water to dis¬ 
solve twelve, sixteen, or even twenty grains of the carbonate, 
when it will have twelve, sixteen, or twenty degrees of 


126 


IMPURITIES OF WATER. 


hardness, according to the number of grains taken into 
solution. 

These salts of lime and magnesia, and of iron, in water, 
have the property of decomposing an equivalent quantity 
of soap, rendering it useless as a detergent; thus, one 
degree or grain of the carbonate neutralizes ten grains of 
soap; two degrees, twenty grains of soap; three degrees, 
thirty grains, etc. 

This source of waste from foul hard waters, which extends 
to the destruction of many valuable food properties, as well 
as to destroying soap, is not sufficiently appreciated by the 
general public. 

It may be safely asserted that a foul hard well water 
will destroy from the family that uses it, more value each 
year than would be the cost in money of an abundant 
supply of water for domestic purposes, from an accessible 
public water supply ; and this refers to purchased articles 
merely, and not to destruction of human health and energy, 
which are beyond price. 

109. Temperatures of Deep Sub-surface Waters. 

—Very deep well and spring waters have, upon their first 
issue, too high a temperature for drinking purposes, as from 
the artesian wells of the Paris basin, which rise at a tem¬ 
perature of 82 c Fall., and as from hot springs, among which, 
for illustration, may be mentioned the Sulphur Springs,. 
Florida, of 70° Fah., the Lebanon Springs, N. Y., of 73° F.; 
and, as extremes of high temperature, the famous geysers 
of the Yellowstone Valley, at a boiling temperature, and 
the large hot spring near the eastern base of the Sierra 
Yevadas and Pyramid Lake, whose broad pool has a tem¬ 
perature of 206°, and central issue 212°. The springs at 
Chaudes Aigues, in France, have a temperature of 176°, 
and the renowned geysers of Iceland, of 212°. 


DECOMPOSING ORGANIC IMPURITIES. 


127 


Artesian wells have temperatures for given depths ap¬ 
proximately as follows: 

TABLE No. 3 6. 

Artesian Well Temperatures. 


Depth in Feet. 

100 

500 

IOOO 

1500 

2000 

2500 

3000 

Temperature, deg. Fah. 

52 

59 

68 

76 

35 

94 

102 


110. Decomposing* Organic Impurities. —If we re¬ 
solve, chemically, a piece of stone, ore, w T ood, fruit, a cup 
of water, or an amputated animal limb, into their simple 
elements within the limits of exact chemical investigation, 
we shall find that their varied compositions and proper¬ 
ties are results of combinations, substantially, of the same 
few elements ; and that the organic substances—that is, such 
as are the result of growth under the influence of their own 
vitality—are composed chiefly of carbon, oxygen, hydrogen, 
and nitrogen, with spare proportions of a few metalloids, 
as above enumerated. The general order of predominance 
of the gases and metalloids is not, however, quite the same 
in mineral as in organic matters. But notwithstanding this 
apparent similarity of chemical compositions, there is a 
quality in organic substances accompanying the vital force, 
that makes it as widely different in essential characteristics 
from simple mineral compounds as life is from death. 

The mysterious properties which accompany only the 
vital force do not submit to analyses by human art. They 
are known only by their results and their effects. 

In the natural decomposition of animal matters, espe¬ 
cially in their stage of putrefaction, their elements are often 
in a condition of molecular activity that will not admit of 
their being safely brought into contact with the human 













128 


IMPURITIES OF WATER. 


circulation, where they will be liable to induce similar con¬ 
ditions. 

Witness the extreme danger to a surgeon who receives 
a minute quantity of animal fluid into a sore upon his hand, 
when dissecting a dead body, even though the life lias been 
extinct but one or two days. 

The excreta of living animals also passes through a 
decomposing transformation, in which stage they cannot 
safely be brought into contact with the human circulation, 
however finely they may be dissolved in water, when re¬ 
ceived. 

The process of decay in dead animal bodies, and of de¬ 
composition of vegetable substances, is quite rapid when 
moisture and an abundance of atmospheric air, or available 
oxygen in any form, are present, and a warm temperature 
promotes the activity of the elements ; hence the same mat¬ 
ter does not long remain in its most objectionable state, but 
from the multiplicity of bodies on every hand, a constant 
source of pollution may be maintained. 

Potable waters, when exposed to those organic matters 
in process of rapid decay, meet perhaps their most fatal 
sources of natural contamination, that are not readily de¬ 
tected by the eye and tongue. 

111. Vegetable Organic Impurities.— Nature around 
us swarms with an abundance of both vegetable and ani¬ 
mal life, in air, in earth, in stream and sea, and therefore 
death is constantly on every hand, and its dissolutions 
meet the waters wherever they fall or flow. There are 
numerous plants, trees, insects, and animals that we recog¬ 
nize day by day, but there are undoubtedly species and 
classes more innumerable above and below, that we can dis¬ 
cover only when our vision is aided by magnifying lenses. 

Upon, the meadow pools and small ponds of the swamps, 


VEGETAL ORGANISMS IN WATER-PIPES. 


129 


species of microscopic fungi, not unlike the mould upon 
decaying fruit, though less luxuriant, are found in abun¬ 
dance by searchers who suspect their presence. To the 
general observer they appear as dust upon the water or 
give to it a slight appearance of opaqueness. 

There are species of fresli-water algae that thrive in 
abundance, peculiar to all seasons, and they are said to have 
been found in the heated waters of boiling spring basins, 
and also in healthy life within an icicle, and they are the last 
of life high up on the mountain slopes, near the borders of 
eternal snows. Ditches, pools, springs, rivers, lakes, and 
dripping grottoes have each their native class. In stagnant 
waters abound the oscillatorise of dull-greenish or dark- 
purplisli or bluish color, forming dense slimy strata, and 
the brighter green zygenemas which iioat or lie entangled 
among the water plants. 

The desmids abound in the early spring of the year, and 
various alga) flourish in, the autumn. A thrifty fungus of 
the genus Noctos frequents the quiet waters of lower New 
England and the Middle States. 

These plants at their dissolution often impart an oily 
appearance, a greenish or brownish color, and a somewhat 
offensive smell to the water. The noctos, while in active 
growth, forms part of the green scum often seen upon the 
surface of still water. The fishy smell and the color which 
they impart to the water in decomposing seems to be largely 
due to an essential oil which they give out when breaking up. 

112. Vegetal Organisms in Water-Pipes. — A 
species of confervse has been found growing and multiply¬ 
ing rapidly within water-pipes, having taken root in the 
fine organic sediment deposited from feeble currents of 
water in the dead ends or in the large mains. These micro¬ 
scopic plants, after maturing in abundance, are detached 


130 


IMPURITIES OF WATER. 


by the current, decompose, and impart an appreciable 
amount of odor and taste to the water, reduce its transpar¬ 
ency and give a slight tinge of color. 

113. Animate Organic Impurities. —The waters are 
not less pregnant with animate than vegetal life. The mi¬ 
croscope has here extended our knowledge of varieties and 
numbers of species also, especially in waters infused with 
organic substances. 

The tiny infusoria were first discovered in strong vegeta¬ 
ble infusions, hence the name given to them; but with the 
extension of microscopical science, the class has been ex¬ 
tended to include a variety of animate existences, from the 
quiet fresh water sponge to the most energetic little creatures 
that battle ferociously in a drop of water. 

Dr. Crace Calvert has shown* that when albumen from 
a new laid egg is introduced in pure distilled water and 
exposed to the atmosphere, minute globular bodies soon 
appear having independent motion. These he denominated 
monads. 

Their appearance was earlier in lake water than in dis¬ 
tilled water, and earliest and most abundant in solutions 
of largest exposure to the atmosphere. 

These monads have diameters of about of an 

inch; in their next successive stage, of about °f ai1 

inch ; and then of about of an inch. He denominates 
them vibrios in the two last stages. Then they change into 
cells, having power to pass over the field of the microscope 
rapidly. 

The albuminous products of decaying leaves and plants 
in water also promote the generation of aquatic life, and 
dead animal substances are almost immediately inhabited 
by a myriad of creatures. 


* Papers read before the Royal Society, London. 








AQUATIC ORGANISMS. 


131 


The discussion upon the question of spontaneous gene¬ 
ration in progress at the opening of our centennial year, is 
adding many new and interesting experimental results to 
the researches of Pasteur and Schroeder, relating to the 
propagation of bacterial life from atmospheric mote germs, 
and the agency of germs in the spread of epidemic contagia. 
Prof. Tyndall and Dr. Bastian, the leading controversialists 
in this discussion, are agreed that both vegetable and animal 
infusions, if exposed to the summer atmosphere, will, ordi¬ 
narily, abound in bacterial life in about three days. 

There are also in the streams and lakes the larger 
zoophytes, mollusca, articulata, and Crustacea, some of which 
are familiar products of the waters, and also fish in great 
variety. 

But all of these do not pass through the objectionable 
putrefactive stage described above. The w r eaker classes 
are food for the stronger, and the smaller of some classes 
food for the larger of the same class. Of the many that 
come into being, comparatively few survive till a natural 
death terminates their existence, but each devours others 
for a substantial part of its own nourishment, and hides, 
fights, or retreats to preserve its own existence. 

114. Propagation of Aquatic Organisms.— A warm 
temperature of both air and water are requisite for the abun¬ 
dant propagation of aquatic life. The presence of a consid¬ 
erable amount of either vegetable or animal impurities in 
the waters seems also a requisite for the lower grades of life. 

How far certain electrical influences in the air and water 
control the results are not yet determined. Certain it is, 
however, that the microscopic creatures sometimes swarm 
suddenly in abundance in quiet lakes and pools, in a seem¬ 
ingly unaccountable manner, remain in abundance for a 
few days, or possibly a few weeks in rare seasons, and then 


132 


IMPURITIES OF WATER. 


as mysteriously disappear. There is a similar appearance 
of microscopic plants, when all the natural conditions favor¬ 
able thereto occur simultaneously, but their coming cannot 
always • be predicted, neither can the time of their disap¬ 
pearance be foretold. 

A very brief existence is allotted to a large share of the 
minute vegetal and animate aquatic beings we have had in 
consideration. Perhaps the greater share of the animate, 
count scarce a single circuit of the sun in their whole term ; 
others soon pass to a higher stage in their existence, and 
are thereafter terrestrial in their habits. 

115. Purifying' Office of Aquatic Life. —One of the 
chief offices of the inferior inhabitants of the waters is to 
aid in their purification by devouring and assimilating the 
dead and decaying organic matters. 

The infusorial animalculae are undoubtedly encouraged 
in their propagation by the presence of impurities so far as 
to be an unmistakable indication of such impurities; and 
they, on the other hand, attack and destroy such impurities 
for their own nourishment, when they are devoured, and 
their devourers devoured by higher existences, till the last 
become food for fish that constitutes a food for man. 

This, and this only, is the proper channel through which 
the decomposing organic impurities in water should reach 
the human stomach, having by Nature’s wonderful pro¬ 
cesses of assimilation been first converted into superior 
living tissues. 

A great variety of fish are daily consumed for our food, 
also of mollusca from salt water, as clams, oysters, and mus¬ 
sels, also of Crustacea, as lobsters, crabs, shrimp, etc.; hence 
we infer that the higher orders of fresh water inhabitants are 
not harmful while living therein, and are nourishing as food, 
if consumed while the influence of their vital force remains. 


ABRASION IMPURITIES. 


133 


The action of oxygen upon organic bodies tends always 
powerfully to decomposition, but is counteracted by the 
vital force. When the vital force ceases then decomposi¬ 
tion soon begins, and then the body acted upon is unfitted 
for the human digestive organs. 

116. Intimate Relation between Grade of Organ¬ 
isms and Quality of Water. —The grade and character 
of the growths in fresh water are almost invariably reliable 
tests of the quality of the water, and if the plants be fine¬ 
grained, firm, and delicate in outline, or the fish trim in 
form, lithe in motion, and fine in flavor, the water is most 
sure to be good. 

117. Animate Organisms in Water-Pipes. —Nearly 
all of the animate aquatic existences must rise frequently 
to the water surface to secure their necessary share of at¬ 
mospheric oxygen. If any of them, not having tracheal 
gills, or their equivalents, to enable them to breathe a long 
time under water, are drawn into the pipes, and are thus 
cut off from their supply of oxygen, they soon perish. 
Then, if the water is not of low temperature, their decom¬ 
position soon commences, and an offensive gas from their 
bodies enters into solution with the water. 

118. Abrasion Impurities in Water. — The most 
prominent sources of the frictional impurities are the banks 
of clay and sand bordering upon the running streams, and 
the plowed fields of the hillside farms. The movement 
of these sedimentary matters in suspension is dependent 
largely upon the force of storms and floods, and in the ma¬ 
jority of streams their movement is rapid toward the sea, 
where they are massed in foundations of lagoons and islands. 

With them are swept away a great bulk of the matured 
products of vegetation that annually ripen in the forest, the 
field, and upon the banks of the streams. 


134 


IMPURITIES OF WATER. 


119. Agricultural Impurities. —It remains now to re¬ 
view in outline the artificial impurities, which are always 
to be shunned if known to be present, and are to be sus¬ 
piciously watched for, as secret poisons lurking in the clear 
and sparkling water. 

These are, it is true, compounds of mineral and organic 
matters, similar in many respects to those already con¬ 
sidered. 

Nature provides prompt acting remedies for such nox¬ 
ious impurities as she presents to the waters, and the 
seasons of most rapid fouling have the most abundant 
purifying resources. But when great bulks of decompos¬ 
ing organic matters are massed and are permitted to foul 
the streams with a blackening flow of disease-inducing 
dregs, such as are washed from fertile gardens, or pour 
from manufactories and sewers, no adequate, prompt, na¬ 
tural remedy is at hand. 

One of the first results of the massing of people together 
is an increase in degree of fertilization of the land of their 
neighborhood, and thus the lands over and through which 
their waters flow are mixed with concentrated decomposing 
vegetable and animal products. 

120. Manufacturing Impurities. — Manufactories, 
especially such as deal with organic products, are prolific 
sources of contamination. Among their operations and 
refuse may be enumerated as prominent polluters, washings 
of wool and vegetable dyes of woollen mills, washing of old 
rags and foul linens of paper-mills, the hair, scrapings, 
bark, and liquors of tanneries, the refuse and liquors of 
glue factories, bone-boiling and soap-works, pork render¬ 
ing and packing establishments, slaughter-houses and gas- 
works. 

121. Sewage Impurities. —Most foul and fearful of all 


IMPURE ICE IN DRINKING WATER. 


135 


the artificial pollutions which ignorant and careless human¬ 
ity permits to reach the streams are the drainage of cesspools, 
sewers, pig-styes, and stable-yards. 

The man who permits his family to use waters impreg¬ 
nated with fecal substances that the bodies of other persons 
or animals have already excreted, and the authorities who 
permit their citizens to use such waters, opens for them 
freely the gates to aches and pains, weaknesses,of body and 
mind, injuries of tissues and blood, attacks of chronic dis¬ 
eases and epidemics, and surely permits destruction of 
their vigor, shortens their average life, and also degenerates 
the entire existence of the generation they are rearing to 
succeed them, whom it is their duty as well as pleasure to 
cherish and protect. 

There is no community, there are very few families, and 
comparatively few animals without disease. In large com¬ 
munities there is rarely a time when some virulent disease 
does not exist. 

The products of the humors and fevers of each individual 
in large part escapes from the body in the feces and urine. 
If drinking water is allowed to absorb these festering mat¬ 
ters, either in the ground or in the stream, it transmits them 
directly to the blood and tissues of other individuals, and a 

c/ 

hundred deaths may result from the evacuations of a single 
diseased person. 

122 . Impure Ice in Drinking Water.— Ice is now 

so generally used in drinking-water in summer, to cool it 
immediately before drinking, that the people should be 
warned against such use of ice gathered from water that 
would have been unfit for drinking before freezing. Chem¬ 
istry has fully demonstrated that ice is not entirely purified 
by the process of crystallization, as has been popularly 
believed. 


136 


IMPURITIES OF WATER. 


Tlie impurities that are in that portion of water that 
freezes, some of which have just been brought from the 
bottom by the vertical circulation that occurs when water 
is chilled at the surface, are caught among the crystals and 
preserved there, as even fresh meats, and fruits might be 
preserved. The process of purification of the water that 
would have gone on by the oxidation of the impurities, is 
checked when they are surrounded by the ice crystals, and 
proceeds again when the ice melts. 

An instance, of much notoriety, of the effects of impure 
ice, was that of the sickness among the numerous guests, 
during the season of 1875, at one of the Rye Beach hotels, 
a popular resort on the New Hampshire coast. 

The sickness here, confined to one hotel in the early part 
of the season, was, after much search by an expert physi¬ 
cian, traced unmistakably to the ice, which was gathered 
from a small stagnant pond, and all the peculiar unplea¬ 
sant symptoms ceased when the source was located and a 
purer supply of ice obtained. 

An analysis of the impure ice in question, by Professor 
W. R. Nichols, gave the following result, by the side of 
which is placed a like analysis of water from Cocliituate 
Lake, for the purpose of comparison : 



Ice from Stagnant 
Pond. 

Water from 
CoCHITUATE 
Lake. 

Grains per U. S. Gal. 

Grains per 
U. S. Gal. 

Ammonia. 

Unfiltered. 

O.OI21 
O.O4IO 

4-55 

3-33 

Filtered. 

O.OI24 

.OO96 

4.01 

1.66 

0.0020 

0.0068 

1.6l 

1.22 

Albuminoid Ammonia. 

Inorganic Matter. 

Organic and Volatile Matter. 

Total solid residue at 212° Fahrenheit.. 
Chlorine.. ; . 

7.88 

5-67 

1.88 

0.495 

2.83 

.18 

Oxygen required to oxidize organic matter. 





















DEFINITION OF POLLUTED WATER. 


137 


123. A Scientific Definition of Polluted Water.— 

Subject, as the sensitive water is, to innumerable deteriora¬ 
ting and purifying influences, in its transformations and 
varied course from the atmosphere to the household foun¬ 
tain, it becomes of the greatest sanitary importance to know 
when the deteriorating influences still predominate, and when 
further purification is essential for the well being of the 
consumers. 

Professor Frankland, an eminent English authority on 
the quality of drinking water, has clearly defined a mini¬ 
mum limit, when, in his opinion, water contains sufficient 
mechanical or chemical impurities, in suspension or solu¬ 
tion, to entitle it to be considered bad, or a polluted 
liquid, viz. : 

(a.) Every liquid which has not been submitted to pre¬ 
cipitation produced by a perfect repose in reservoirs of suf¬ 
ficient dimensions during a period of at least six hours; or 
which, having been submitted to precipitation, contains in 
suspension more than one part by weight of dry organic 
matter in 100,000 parts of liquid ; or which, not having been 
submitted to precipitation, contains in suspension more 
than 3 parts by weight of dry mineral matter, or 1 part by 
weight of dry organic matter, in 100,000 parts of liquid. 

(b.) Every liquid containing in solution more than 2 
parts by weight of organic carbon or 3 parts of organic 
nitrogen in 100,000 parts of liquid. 

(c.) Every liquid which, when placed in a white porce¬ 
lain vessel to the depth of one inch, exhibits under daylight 
a distinct color. 

(cl.) Every liquid which contains in solution, in every 
100,000 parts by weight, more than 2 parts of any metal, 
except calcium, magnesium, potassium, and sodium. 

(e.) Every liquid which in every 100,000 parts by weight 


138 


IMPURITIES OF WATER. 


contains in solution, suspension, chemical combination, or 
otherwise, more than 0.5 of metallic arsenic. 

(/.) Every liquid which, after the addition of sulphuric 
acid, contains in every 100,000 parts by weight more than 
1 part of free chlorine. 

(g.) Every liquid which, in every 100,000 parts by 
weight, contains more than 1 part of sulphur, in the state 
of sulphuretted hydrogen or of a soluble sulpliuret. 

([h .) Every liquid having an acidity superior to that pro¬ 
duced by adding 2 parts by weight of hydrochloric acid to 
1,000 parts of distilled water. 

(i.) Every liquid having an alkalinity greater than that 
produced by adding 1 part by weight of caustic soda to 
1,000 parts of distilled water. 

(j.). Every liquid exhibiting on its surface a film of 
petroleum or hydrocarbon, or containing in suspension hi 
100,000 parts, more than 0.5 of such oils. 



. ( _ 


t : Ji 



PUMPING STATION, NEW 


BEDFORD. 





















































































































































CHAPTER IX. 

WELL, SPRING, LAKE, AND RIVER SUPPLIES. 

It remains now to add to tliese general theories respect¬ 
ing the parity of water some special suggestions relating to 
the selection of a potable water. 

WELL WATER. 

124. Location for Wells.— We have seen that the 
source of water supply to wells is, immediately, the rain, 
and that in the vicinity of dense populations the rain reaches 
the surface of the earth, already polluted by the impurities 
of the town atmosphere. 

In the open country, the water reaches the ground in a 
tolerably pure condition, and by judicious selection of a 
site for a well, its water may usually be procured of excel¬ 
lent quality. Country wells must, however, be entirely 
separated from the drainage of the stable yards, muck 
heaps, and house sewerage, and from soakage through 
highly fertilized gardens. 

In towns, surface soils are continually recipients of 
household refuse, manures, and sewer liquors, and of dead 
and decaying, animal matters. 

These have, by abundant examples, been proved to be 
the most dangerous of the ordinary contaminations of shal¬ 
low wells. 

The strictly mineral impurities, to which all wells are 
to some extent subject, are not usually injurious to human 
constitutions, though in districts where lime is present in 


140 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 

the soil in considerable quantity, the resulting hardness is 
inconvenient and indirectly expensive. 

An intelligent examination of the positions, dip, and 
porosity of the earth’s superstrata in the vicinity of a pro¬ 
posed well will be a more infallible guide to its location 
where it will yield an unfailing, abundant, and wholesome 
supply, than will reliance upon “hazel forks” and “divin¬ 
ing rods,” in which the superstitious have evinced faith and 
by which they have often been deceived. 

125. Fouling* of Old Wells. —The table of analyses 
of well-waters above presented (page 121, et seq.) indicates 
that the old wells of towns are among the most impure 
sources of domestic water supply. 

The continued increase in the hardness of well-water as 
the population about them becomes more dense, indicates 
that this increase is due to the salts of the dissolved organic 
refuse with which the ground in time becomes saturated. 

Mr. F. Sutton, an English analyst, states, that “out of 
four hundred and twenty-nine samples of water sent him 
from wells in country towns, he was obliged to reject three 
hundred and seven as unfit for drinking.” Another Eng¬ 
lish chemist states that “ much of the well-water he is called 
upon to examine proves to be more fit for fertilizing pur¬ 
poses than for human consumption.” 

Prof. Chandler, President of the New York City Board 
of Health, and Professor of Chemistry in the School of 
Mines, Columbia College, remarked : “In many cases, from 
the proximity of cesspools and privy vaults, the well-water 
becomes contaminated with filtered sewage, matters which, 
while they hardly affect the taste or smell of the water, 
have nevertheless the power to create the most deadly dis¬ 
turbances in the persons who use the waters.” 

Hall’s “Journal of Health” remarked that, “in the 


HARMLESS IMPREGNATIONS. 


141 


autumn many wells, which supply families with drinking 
and cooking water, get very low and their bottoms are cov¬ 
ered with a line mud, largely the result of organic decom¬ 
positions, also containing poisonous matters of a very con¬ 
centrated character. The very emanations from this well 
mud are capable of causing malignant fevers in a few hours ; 
hence many families dependent on well-waters are made 
sick during the fall of the year by drinking these impreg¬ 
nated poisons, and introducing them directly into the circu¬ 
lation. Many obscure ailments and ‘dumb agues’ are 
caused in this way.” 

SPRING WATERS. 

12G. Harmless Impregnations. —The impurities of 
spring water are chiefly mineral in character, derived from 
the constituents of the earths through which their waters 
percolate. Among the most soluble of the earths are mag¬ 
nesium, calcium, potassium, and sodium, and these appear 
in spring waters as carbonates, bicarbonates, chlorides, 
sulphates, silicates, phosphates, and nitrates, and are usu¬ 
ally accompanied by an oxide of iron and a minute quan¬ 
tity of silica. 

The above earths are harmless, and are, in fact, consid¬ 
ered beneficial in drinking waters, when present in moderate 
quantities, or not exceeding eight or ten grains per gallon. 
Most persons are familiar with the medicinal properties of 
the carbonate of magnesia, a mild cathartic, and of its sul¬ 
phate (Epsom salts), a mild purgative, and with the carbon¬ 
ate and nitrate of potassa (pearlash and saltpetre) in the 
arts, and with the medicinal properties of the bromide of 
potassium, a mild diuretic. 

Sodium is more familiarly known as common sea-salt, 
and calcium as common lime, of which it is the base, and 


142 


WELL, SPRING, LAKE, AND RIVER SUPPLIES. 


silica as the base of quartz or common sand. Spring waters 
are, by their passage through the earth, thoroughly filtered 
and relieved of suspended impurities, and therefore appear 
as the most clear and sparkling of all natural waters. 

In the selection of a spring water, it is to be specially 
observed that it is free from impregnation by decaying 
organic matters. 

127. Mineral Springs. —In illustration of the facts 
that clearness to the eye is not evidence of purity, or min¬ 
eral impregnation of the most usual character immediately 
dangerous to the constitution, we append a few analyses of 
well-known mineral spring waters, with quantities of ingre¬ 
dients expressed in grains per U. S. gallon. (See page 143.) 

This formidable array of chemical ingredients indi¬ 
cates that the waters have taken into solution the familiar 
minerals, magnesia, common salt, lime, iron, potash, sul¬ 
phur, quartz, and clay, and the gases, oxygen, hydrogen, 
nitrogen, and carbonic acid. 

It is much to be regretted that supplies from good springs 
are usually so limited in quantity. 

The water supply of Dubuque, Iowa, is obtained from 
an adit pierced into the blutf near the city. The operations 
of miners working in the bluff were seriously impeded by 
water, and they relieved themselves by tunneling in from 
the face of the bluff, and thus underdraining the mine. In 
so doing, they intercepted numerous percolating streams of 
water. This water is now utilized for the supply of the 
city. 

LAKE WATERS. 

128. Favorite Supplies.— Fresh water lakes and deep 
ponds, whose watersheds have extents equal to at least ten 
times their water surfaces, are ordinarily, of all ample 


Analyses of Mineral Spring Waters. 


MINERAL SPRING WATERS. 


143 


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144 


WELL, SPRING, LAKE, AND RIVER SUPPLIES. 


sources, least liable to objectionable impregnation in harm¬ 
ful quantity. When such waters have been imprisoned in 
their flow, by the uplifting of the rock foundations of the 
hills across some resulting valley, or by more recent crowd¬ 
ing by ice-fields of masses of rock and earth debris into a 
moraine dam, they are bright and lovely features in their 
landscapes, and favorite sources of water-supplies. 

The accomplishments of scientific attainments are not 
requisite to enable the intelligent populations to discover 
in these waters wholesomeness for human draughts and 
adaptability to quench thirsts. 

When such waters are deep, and have a broad expanse 
and bold shores, nature is ever at work with ram and wind 
and sunshine, maintaining their natural purity and sparkle. 

129. Chief Requisites.— The prime requisites in lakes, 
when to be used for domestic supplies, are abundant in¬ 
flow and outflow , that will induce a general circulation; 
abundant depth , that will maintain the water cool through 
the heats of summer and hinder organic growth; and a 
broad surface , which the wind can press upon, and roll, 
and thus stir the water to its greatest depths. 

These are features opposed to quietude, shallowness, 
and warmth, which w r e have seen (§ 114) to be promoters of 
excesses of vegetal and animal life, accompanied by a very 
objectionable mass of vegetable decay and animal decom¬ 
position. Fortunately, the shallow waters are oftenest at 
the upper ends, opposite to the usual points of draught from 
the lake, or in indented bays along the sides, from whence 
their vegetal products are least liable to reach the outflow 
conduit. 

130. Impounding. —When supplying lakes have mod¬ 
erate drainage areas in proportion to the total volume of 
water required from them, it is then necessary to place the 


PLANT GROWTH. 


145 


draught conduit below their natural surface or to raise 
their natural surface by a dam at their outlet, to avail of 
their storage, thus in a degree changing their condition of 
nature into the artificial condition of impounding reser¬ 
voirs. 

The theory of volume of supply from given drainage 
areas (§ 53), and the theory of making available a large 
proportion of the rainfall by impounding (§ 75), have 
already been discussed in their appropriate sections. 

Important results, affecting the purity of the water, may 
follow from the disturbance of the long-maintained condi¬ 
tions of the shores, analogous to those of the construction 
of artificial impounding reservoirs in valleys, by embank¬ 
ments across the outflow streams. 

The waves, of natural broad lakes that have but little 
rise and fall, have long since removed the soil from large 
portions of their shores, leaving them paved with boulders 
and pebbles, which the ice, if in northern latitudes, has 
crowded into close rip-raps, and the removed soil has been 
deposited in the quiet shallow bays. 

Upon the paved shores the lack of vegetable mold and 
the dash of the waters are obstacles to the growth of vege¬ 
tation. 

131. Plant Growth. —If, under the new conditions, the 
waters are drawn down in the summer, the wave power re¬ 
duced, the shallow bottoms of the bays uncovered, and an 
entire shore circuit of vegetable deposit exposed to the hot 
sun, a mass of luxuriant vegetation at once springs into ex¬ 
istence upon this uncovered bottom, and the greater its thrift 
the more rapid its decay, and the more objectionable its 
gaseous emanations that will enter into solution in the water. 

Such growths and transformations may continue to re¬ 
peat themselves through several successive years, and to 


146 


WELL, SPRING, LAKE, AND RIVER SUPPLIES. 


some extent continuously. Under the former conditions of 
deeper water the plant life was of less abundance, of less 
thrifty growth, and of less rapid decay, and the natural 
processes of purification were adequate to maintain the 
natural purity of the water. 

Stimulated vegetable growths result in quick decay and 
the production of vegetable muck, the foulest solid product 
of vegetable decompositions in water. Slow decompositions 
of vegetable matter in water rarely affect the water to a 
noxious degree, and result in the production of a peat de¬ 
posit almost entirely free from deleterious qualities in the 
water. 

The presence of the fishy or cucumber odor is evidence 
that the water, or a considerable portion of it, has been too 
warm for stored potable water ; and that there is too much 
of shallow margin, or that the storage lake has received too 
much of meadow drainage. It is not, as many have sup¬ 
posed, an evidence of dead fish in the reservoir, but an effect 
tending to drive the higher orders of the fish more closely 
about the springs or inflowing streams. 

132. Strata Conditions. —The winds assist the ready 
escape of the odorous gases when they have risen near to 
the surface, and the stratum of water of greatest purity, in 
summer, is usually a little below the surface, and would be 
at the surface were it not for the microscopic organisms that 
exist there, and the floating matters. 

The change of density of water with change of tempera¬ 
ture produces a remarkable effect in autumn. Water is at 
its greatest density at the temperature just above freezing 
(39°2 Fall.), and when the frosts of autumn chill the surface 
water it is then heavier than the water below, and sinks, dis¬ 
placing the bottom water ; and the vertical circulation, stir¬ 
ring up the whole body, continues until the surface is sealed 


PLANT AND INSECT AGENCIES. 


147 


by ice, when quiet again reigns at the bottom. This action 
stirs up the bottom impurities, and often makes them par¬ 
ticularly offensive in autumn, even more than in mid¬ 
summer. 

In the case of new flowage of artificial reservoirs over a 
meadow bottom, the live vegetable growth has all to go 
through a certain chemical transformation, the influence of 
which upon the water is often detectable, for a time, by the 
sense of smell. This action in the water may be consider¬ 
ably reduced by first burning thoroughly the whole surface, 
and destroying the organic life and properties, leaving only 
the mineral ash. 

The breaking up of the vegetable fibres, if undestroyed 
by fire, and their deposition in the quiet, shallow bays, 
encourages the growth of aquatic plants, and, indirectly, 
animal life there. 

The protection of the shores by high water in winter, and 
their exposure by drawing down the water in summer, is 
favorable to aquatic growths upon them, as in the above- 
mentioned lake examples. 

133. Plant and Insect Agencies. —In cases of ex¬ 
cessive growths of either or both vegetal and animal life, 
their products are liable to be drawn into the outflow con¬ 
duit and the distribution pipes, where their presence becomes 
disagreeably evident by the gaseous “fishy” or “cucum¬ 
ber” odors liberated when the water is drawn from 
faucets. 

When conditions are favorable for the production of 
either vegetal or animal life alone, in excessive abundance, 
disagreeable effects, especially if the excess be animal, are 
almost certain to follow, since both are among the active 
agents employed by nature in the purification of water, and 
natural laws tend to preserve the due balance in their 


148 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 

growth, the one being producers of oxygen and the other 
of carbon. 

Newly flowed collecting or storage reservoirs should be 
promptly stocked with a tine grade of fish, that will feed 
upon and prevent the overabundance of the Crustacea, 
which in turn will consume the organic decompositions, and 
prevent their diffusion through the waters. 

134. Preservation of Purity. —General observation 
teaches that neither vegetation or any species of the infu¬ 
soria flourish to an objectionable extent in fresh waters in 
the temperate zone where the depth exceeds about ten feet, 
though it is true that insects are liable to swarm upon the 
surface of all waters that arrive at a high temperature. 
Stored waters, for domestic purposes, ought to have in our 
American climate, depths of not less than tw T elve feet. 

To insure purity of water, so far as protection from its 
own products is concerned, it is necessary that the shallow^ 
waters be cut off by embankments, or that they be deep¬ 
ened, or that their place be supplied by clean sand or 
gravel filling, raised to a level above high water. It is fre¬ 
quently advisable, also, that the shores of artificial impound¬ 
ing reservoirs of moderate extent be provided with an 
equivalent for the natural rip-rap provided by nature 
around natural flakes. 

Each of the above expedients has been successfully 
adopted by the writer in his own practice. 

Fig. 7 is an illustration of the revetment of stone sur¬ 
rounding the reservoir of the Norwich, Conn., w T ater-works. 
The reservoir in this case is two and one-half miles out 
from the city, and fills the office of both a gathering and 
distributing reservoir, for a gravitation supply. Its circum¬ 
ference is tw r o and one-quarter miles, and this revetment 
protects the shore of the entire circuit. Its height above 


NATURAL CLARIFICATION. 


149 


Fig. 7. 



high water, in the vicinity of the dam, is four feet, and in 
the upper part of the valley three feet. 

If the supplying streams of a small lake bring with them 
much vegetable matter in suspension, and the flow reaches 
the conduit before complete clarification by natural pro¬ 
cesses is effected, some method of artificial filtration of the 
w T ater will be necessary, the details of which will be dis¬ 
cussed hereafter. 

135. Natural Clarification. —The various sources of 
chemical impregnation to which waters reaching lakes, usu¬ 
ally are subject, whether flowing over or through the earth, 
have been already herein discussed (§ 101, et seq.\ so that 
persons of ordinary intelligence and information may detect 
them, and form a tolerably accurate estimate of their harm- 
fulness, and if they ought to be considered objectionable 
when they are to be gathered in a lake and there subjected 
to the processes in Nature’s favorite laboratory of purifi¬ 
cation. 

Waters flowing in the brooks from the wooded hills and 
the swamps almost always come down to the lakes highly 
charged with the coloring matter and substances of forest 
leaves and grasses, and not unfrequently have a very per- 



































150 


WELL, SPRING, LAKE AND RIVER SUPPLIES. 


ceptible reddisli or chocolate hue. The waters are soon 
relieved of these vegetable impurities by natural processes 
in the lake, and their natural transparency and sparkle is 
restored to them. Sunlight has been credited with a strong 
influence in the removal of color from water. The chemical 
transformation already begun upon the hills is continued in 
the lake, and the atmospheric oxygen aids in releasing the 
gases of the minutely subdivided vegetable products pro¬ 
ducing the color, when the mineral residues have sufficient 
specific gravity to take them speedily to the bottom. The 
winds are the good physicians that bring the restoring 
remedies. 

Ponds and lakes often receive a considerable part of 
their supply from springs along their borders, whose waters 
have received the most perfect natural clarification. Such 
springs, from quartzose earths, yield waters of the most 
desirable qualities. 

13G. Great Lakes. —When lakes, on a scale of great 
inland seas, like those lining our northern boundary, upon 
which great marts of trade are developing, are at hand, 
many of the above supposed conditions belonging to 
smaller lakes and ponds, are entirely modified. 

In such cases the cities become themselves the worst 
polluters of the pure waters lying at their borders, and 
they are obliged to push their draught tunnels or pipes 
beneath the waters far out under the lakes to where the 
water is undefiled. 

This system was inaugurated on a great scale by Mr. 
E. S. Clieesboro, C.E., for Chicago, and followed by the 
cities of Cleveland, Buffalo, and with submerged pipe by 
Milwaukee. 

137. Dead Lakes. —The waters of the Sinks, or Dead 
Lakes of the Utah, Nevada, and southern California, Great 


METROPOLITAN SUPPLIES. 


151 


Desert, from which there are no visible outlets, are notable 
exceptions to general conditions of lake waters. Here the 
salts gathered by the inflowing waters, for centuries, which 
evaporating vapors can not carry away, have been accu¬ 
mulating, till the waters are nauseating and repugnant. 

The skill of the well-borer must aid civilization when 
these desert regions are to become generally inhabitable. 

RIVER WATERS. 

138. Metropolitan Supplies.— Rivers are of necessity 
the final resort of a majority of the principal cities of the 
world for their public water supply. The volume of water 
daily required in a great metropolis often exceeds the com¬ 
bined capacity of all the springs, brooks, and ponds within 
accessible limits, and supplies from wells become impos¬ 
sible because of lack of capacity, excessive aggregate cost, 
and the sickening character of their waters. 

Since rivers occupy the lowest threads of the valleys in 
which they flow, their surfaces are lower than the founda¬ 
tions of the habitations and warehouses along their banks. 

Their waters have therefore usually to be elevated by 
power for delivery in the buildings, the expense of conduct¬ 
ing their waters from their sufficiently elevated sources being 
greater far than the capitalized cost of the artificial lift 
nearer at hand. 

The theories by which the minimum flow of the stream 
(§ 53), and the maximum demand for supply (§ 19), are 
determined and compared have been already herein dis¬ 
cussed ; so we now assume that the supplies have, after 
proper investigation, been determined ample, and also that 
the geological structure (§ 106) of the drainage area is found 
to present no impregnating strata precluding the use of its 


152 


WELL, SPRING, LAKE, AND RIVER SUPPLIES. 


waters for domestic and commercial purposes, or in tlie 
chemical arts. 

139. Harmless and Beneficial Impregnations.— 

The natural organic impurities of rivers are seldom other 
than dissolving vegetable fibres washed down from forests 
and swamps, and these are rarely in objectionable amount; 
and the natural mineral impurities in solution are usually 
magnesia, common salt, lime, and iron, and, in suspension, 
sand and clay. The lime, sand, and clay are easily detect- 
ible if in objectionable amount, and the remaining natural 
mineral impregnation are quite likely to be beneficial 
rather than otherwise, since they are required in drinking 
water to a limited extent to render them palatable, and for 
promotion of the healthy activity of the digestive organs, 
and the building up of the bones and muscles of our bodies. 

140. Pollutions. —We reiterate that it is the artificial 
impur ities that are the bane of our river waters. Manufac¬ 
tories, villages, towns, and cities spring up upon the river- 
banks, and their refuse, dead animals, and sewage are 
dumped into the running streams, making them foul potions 
of putrefaction and destruction, when they should flow clear 
and wholesome according to the natural laws of their crea¬ 
tion and preservation. 

141. Sanitary Discussions. —The prolific discussion 
upon the sanitary condition of the water of the river 
Thames, England, since the report of the Royal Commis¬ 
sion of 1850, has brought out a variety of conflicting opin¬ 
ions in regard to the efficiency of natural causes to destroy 
sewage impurities in water. 

About one-half the population of London, or one-half 
million persons, received their domestic water supply from 
the Thames in 1875. The drainage area above the pump¬ 
ing stations is about 3675 square miles, and the minimum 


SANITARY DISCUSSIONS. 


153 


summer flow is estimated to be about 350,000,000 imperial 
gallons daily, and of tliis flow about 15,000,000 gallons is 
pumped daily by tlie water companies. Upon the Thames 
watershed above the pumping stations there resides a popu¬ 
lation of about 1,000,000 persons, including three cities of 
over 25,000 persons each, three cities of from 7000 to 10,000 
persons each, and many smaller towns and villages. The 
whole of the river and its principal tributaries are under 
the strictest sanitary regulation which the government is 
able to enforce, notwithstanding which a great mass of 
sewage is poured into the stream. 

Yet it is claimed by eminent authority that the Thames 
water a short distance above London is wholesome, pala¬ 
table, and agreeable, and safe for domestic use. 

A remark by Dr. H. Letheby, medical officer of health 
for the city of London until his decease in the spring of 
1876, gives a comprehensive summary of the argument in 
favor of the Thames water, viz.: “I have arrived at a very 
decided conclusion that sewage, when it is mixed with 
twenty times its volume of running water and has flowed a 
distance of ten or twelve miles, is absolutely destroyed: 
the agents of destruction being infusorial animals, aquatic 
plants and fish, and chemical oxydation.” 

Several eminent chemists testify that analyses detect no 
trace of the sewage in the Thames near London. Sir Benja¬ 
min Broodie, Professor of Chemistry in the University of 
Oxford, remarked in his testimony upon the London water 
supply: “I should rely upon the dilution quite as much, 
and more, than upon the destruction of the injurious 
matter. 

Dr. C. F. Chandler, President of the New York Board 
of Health, and Professor of Chemistry in the School of 
Mines, Columbia College, has in his own writings quoted 


154 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 

many eminent authorities,* with apparent indorsement of 
their conclusions, supporting the theory of the wholesome¬ 
ness and safety of the Thames water as a domestic supply 
for the city of London. 

142. Inadmissible Polluting Liquids.— The Par¬ 
liamentary Rivers Pollution Committee, when investigating 
the subject of the discharge of manufacturing refuse and 
sewage into the English rivers, Mersey and Kibble, and the 
possibility of the deodorization and cleansing of the refuse 
by methods then available, suggested f that liquids con¬ 
taining impurities equal to or in excess of the limiting quan¬ 
tity defined by Prof. Frankland (vide § 12.3, p. 137), be 
deemed polluting and inadmissible into any stream. 

143. Precautionary Views. — On the other hand, 
many physicians, chemists, and engineers, whose scientific 
attainments give to their opinions great weight, emphatically 
protest against the adoption or use of a source of domestic 
water supply that is at all subject to contamination by 
sewage or putrefying organic matters of any kind. 

There are certain laws of nature that have for their 
object the preservation of human life to its appointed ma¬ 
turity, which we term instinct, as, for instance, involuntary 
grasping at a support to save from a threatened fall; invol¬ 
untary raising the arm to protect the eye or head from a 
blow; involuntary sudden withdrawal of the body from 
contact with a hot substance that would burn. There is also 
an instinctive repugnance to receiving any excrementitious 
or putrefying animal substance, or anything that the eye or 
sense of smell decides to be noxious, upon the tongue or 
into the system. It is not safe to overlook or subdue the 
natural instincts created within us for our preservation. 


* Public Healtli Papers of American Public Health Association, vol. i. 
f First Report. R. P. C., 1868, vol. i, p. 130. 



PRECAUTIONARY VIEWS. 


155 


Following are a few opinions supporting tlie cautionary 
side of the question : 

4 ‘ Except * in rare cases, water which holds in solution a 
perceptible proportion of organic matter becomes soon 
putrid, and acquires qualities which are deleterious. It is 
evident that diarrhoea, dysentery, and other acute or chronic 
affections have been induced endemically by the continued 
use of water holding organic matter in large proportions, 
either in solution or in suspension. It is admitted, as the 
result of universal observation, that the less the quantity of 
organic matter held by the water we drink, the more whole¬ 
some it is.” 

“Nof one has conclusively shown that it is safe to trust 
to dilution, storage, agitation, filtration, or periods of time, 
for the complete removal from water of disease-producing 
elements, whatever these may be. Chemistry and micro¬ 
scopy cannot and do not claim to prove the absence of these 
elements in any specimen of drinking water.” 

u ItJ is a well-received fact, that decomposing animal 
matter in drinking water is a fertile producer of intestinal 
diseases.” 

Dr. Wolf (in Der Untergrund und das Frinkwasser der 
Stadte, Erfurt, 1873) gives a large number of cases, which 
prove conclusively that “bad water produces diarrhoea, 
and can propagate dysentery, typhoid fever, and cholera, 
and that such water is frequently clear, fresh, and very 
agreeable to the taste.” 

Dr. Lyon Playfair, of London, remarks: “The effect of 


* Boutron and Boudet. Annual of French Waters, 1851. 

f Testimony of Dr. R. A. Smith before the Royal Commission of Water 
Supply of London. 

x Report of Medical Commission on Additional Water Supply for Boston, 
1874. 





156 


WELL, SPRING, LAKE, AND RIVER SUPPLIES. 


organic matter in the water depends very much upon the 
character of that organic matter. If it be a mere vegetable 
matter, such as comes from a peaty district, even if the 
water originally is of a pale sherry color, on being exposed 
to the air in reservoirs, or in canals leading from one reser¬ 
voir to another, the vegetable matter gets acted upon by the 
air and becomes insoluble, and is chiefly deposited, and 
what remains has no influence on health. But where the 
organic matter comes from drainage, it is a most formid¬ 
able ingredient in water, and is the one of all others that 
ought to be looked upon with apprehension when it is from 
the refuse of animal matter, the drainage of large towns, 
the drainage of any animals, and especially of human 
beings.” 

The Massachusetts State Board of Health, in their fifth 
annual report, remarking upon the joint use of watercourses 
for sewers and as sources of water supply for domestic use, 
remarks: “We believe that all such joint use is to be 
deprecated.The importance of this matter is under¬ 

rated for two reasons: first, because of the oft-repeated 
assertion, made on the authority of Dr. Letlieby, ‘ that if 
sewage-matter be mixed with twenty times its bulk of ordi¬ 
nary river water, and flow a dozen miles, there is not a 
particle of that sewage to be discovered by chemical 
means secondly, because of the feeling that to be in any 
w r ay prejudicial to health, a water must contain enough 
animal matter to be recognized readily by chemical tests— 
enough, in fact, to be expressed in figures.” 

144. Speculative Condition of the Pollution 
Question.— Sanitary writings have abounded with dis¬ 
cussions of this subject during the last decade ; still, look¬ 
ing broadly over the field of discussion, it is evident that 
the leading medical and chemical authorities have not 



SPONTANEOUS PURIFICATION. 


157 


agreed upon the limit for any case, or class of cases, when 
water becomes noxious or harmful. 

Some of the consumers of the waters of the Thames in 
England and of the Mystic and Charles rivers in New Eng¬ 
land, have evinced a remarkable faith in the toughness of 
human constitutions. 

The whole subject of water contamination remains as 
yet rather physiologically speculative than chemically ex¬ 
act. It is earnestly to be desired that the present experi¬ 
mental practice upon human constitutions, so costly in 
infantile life, may soon yield a sufficiency of conclusive 
statistics, or that science shall soon unveil the subtle and 
mysterious chemical properties of organic matters, at least 
so far as they are now concealed behind recombinations, 
reactions, and test solutions. 

145. Spontaneous Purification. —The river courses 
are the natural drainage channels of the lands, and it can¬ 
not but be expected that a considerable bulk of refuse, from 
populous districts, will find its way to the sea by these 
channels, however strict the sanitary regulations for the 
preservation of the purity of the streams. Therefore it is a 
matter of high scientific interest, and in most cases of great 
hygienic and national importance, to determine what pro¬ 
portion of the organic refuse is destroyed beyond the possi¬ 
bility of harm to animals that drink the water, by spon¬ 
taneous decomposition, and what proportion remains in 
solution and suspension. 

In ordinary culinary and chemical processes we find 
that temperature has an important influence upon the dis¬ 
solving property of water. Water of temperature below 
60° Fall, dissolves meats, vegetables, herbs, sugar, or gum, 
slowly, comparatively, and a cold atmosphere does not pro¬ 
mote decomposition of organic matter. We therefore infer 


158 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 

that a temperature of both atmosphere and water as high, 
or nearly as high, as 60° Fall, are required to promote 
rapid oxydation of the organic impurities in water. In 
winter the process must proceed slowly, and if the stream 
is covered by ice, be almost suspended. Agitation of the 
water is absolutely essential to the long-maintained pro¬ 
cess of oxydation, in order that the water may continue 
charged with the necessary bulk of oxygen in solution ; 
therefore weirs across the stream, roughness of the bed and 
banks of the stream, and rapidity of flow are essential ele¬ 
ments in rapid oxydation. 

Dr. Sheridan Muspratt remarks,* in respect to this spoils 
taneous purification of river waters containing organic mat¬ 
ters : “As a general rule, the carbon unites with oxygen to 
form carbonic acid ; and with hydrogen to form marsh gas 
or carbide of hydrogen ; hydrogen and oxygen unite to 
form water; nitrogen and oxygen with hydrogen to form 
ammonia ; sulphur with hydrogen to form sulphide of hy¬ 
drogen ; phosphorus with hydrogen to form phosphide of 
hydrogen. 

‘ 4 The latter two are exceedingly offensive to the sense of 
smell, and are, moreover, highly poisonous. Thus in the 
spontaneous decomposition of the organic matter contained 
in water, there are produced carbonic acid, carbide of hy¬ 
drogen, ammonia, sulphide of hydrogen, and phosphide of 
hydrogen. These are the recognized compounds ; but when 
it is borne in mind that the gaseous emanations of decom¬ 
posing animal matters are infinitely more offensive to the 
sense of smell and injurious to health than any of the gases 
above mentioned, or of any combination of them, it can 
only be concluded that the effluvia of decaying organic 


* Chemistry, Theoretical, Practical, and Analytical : Glasgow. 



A SUGAR TEST OF WATER. 


159 


matter contains other constituents, of which the true char¬ 
acter has not yet been determined.” This chemical puri¬ 
fication is assisted by vegetal absorption and animalculine 
consumption. 

44G. Artificial Clarification. —While water subjected 
at all to organic, especially drainage or animal impurities, 
should be avoided, if possible, for domestic consumption, 
it should, on the other hand, when necessarily submitted 
to, be clarified before use, of its solids in suspension, by 
precipitation, deposition in storage or settling basins, or by 
one of the most thorough processes of filtration. 

147. A Sugar Test of tlie Quality of Water. —The 
Pharmaceutical Journal quotes Heisclf s simple sugar test 
for water, as follows: 

“Good water should be free from color, unpleasant 
odor and taste, and should quickly afford a good lather 
with a small proportion of soap. 

“ If half a pint of the water be placed in a clean, color¬ 
less glass-stoppered bottle, a few grains of the best white 
lump-sugar added, and the bottle freely exposed to the day¬ 
light in the window of a warm room, the liquid should not 
become turbid, even after exposure for a week or ten days. 
If the water becomes turbid, it is open to grave suspicion 
of sewage contamination ; but if it remain clear, it is 
almost certainly safe. 


\ 







. 





















































STAND-PIPE 


BOSTON 





































































SECTION II. 

Flow of Water through Sluices, Pipes and Channels. 


CIIAPTEE X. 

WEIGHT, PRESSURE, AND MOTION OF WATER. 

148. Special Characteristics of Water. —If we con¬ 
sider those qualities of water that have reference to its 
weight, its pressure, and its motion , we shall observe, espe¬ 
cially : That the rotume of the liquid is composed of an 
immense number of minute particles; that each particle 
has weight individually ; that each particle can receive 
and transmit the effect of weight, in the form of pressure, 
in all directions; and that the particles move past and 
upon each other with very slight resistance. 

We are convinced by the sense of touch that the parti¬ 
cles of a body of water are minute, and have very little 
cohesion among themselves or friction upon each other, 
when we put our hand into a clear pool and find that the 
particles separate without appreciable resistance ; and also 
by the sense of sight, when we see fishes and insects, and, 
with the aid of the microscope, the tiny infusorise, moving 
rapidly through the water, without apparent effort greater 
than would be required to move in air. 

11 




162 


WEIGHT, PRESSURE, AND MOTION OF WATER 


149. Atomic Theory. —Ancient records of scientific 
research inform ns that the study of the divisibility and 
nature of the particles of matter occupied, long ago, the 
most vigorous minds. It is twenty-two centuries since 
Democritus explained the atomic theory to his fellow- 
citizens, and taught them that particles of matter are capa¬ 
ble of subdivision again and again, many times beyond the 
limit perceptible to human senses, but that finally the atom 
will be reached, which is indivisible, the unit of matter. 
Anaxagoras, the teacher of Socrates, maintained, on the 
contrary, that matter is divisible to infinity, and that all 
parts of an inorganic body, to infinite subdivision, are simi¬ 
lar to the whole. This latter theory has not been generally 
accepted. The whole subject of the nature of matter, in its 
various conditions, forms, and stages of progress, has main¬ 
tained its interest through the succeeding centuries, and is 
to-day a favorite study of philosophers and theme of dis¬ 
cussion in lecture halls. 

150. Molecular Theory. —Modern research has dem¬ 
onstrated that the unit of water is composed of at least two 
different substances, and therefore is not an atom. The 
unit is termed a molecule, and, according to the received 
doctrine, the foundation of each molecule of water is two 
molecules of hydrogen and one molecule of oxygen. These 

* latter molecules may possibly be ultimate atoms. 

The theory is advanced that each molecule of water is 
surrounded by an elastic atmosphere, and by a few that it 
is itself slightly elastic. 

Sir William Thompson estimated that between five hun¬ 
dred millions and five thousand millions of the molecules 
of water may be placed side by side in the space of one 
lineal inch. To enable us to detect the outline of one of 
these molecules, our most powerful microscope must have 


INFLUENCE OF CALORIC. 


163 


its magnifying power multiplied as many times again, or 
squared. 

A film of water flowing through an orifice one-hundredth 
of an inch deep, or about the thickness of this leaf, would 
be, according to the above estimate, from five to fifty mil¬ 
lion molecule diameters in depth. It is impossible to com¬ 
prehend so infinitesimal a magnitude as the diameter of one 
of these molecules, so we shall be obliged to imagine them 
so many times magnified as to resemble a mass of transpa¬ 
rent balls, like billiard balls, for instance, or similar spheres, 
and to consider them while so magnified. 

151. Influence of Caloric.— There is also a theory, 
very generally accepted, that the molecules of water, more 
especially their gaseous constituents, are constantly subject 
to the influence of caloric, the cause of heat, and are in 
consequence in incessant compound motion, both vibratory 
and progressive, and that they are constantly moving past 
eacli other, progressing with wavy motion, or are rebound¬ 
ing against each other, and against their retaining vessel. 

This motion may be partially illustrated by the motion 
of a great number of smooth, transparent, elastic balls, in a 
a vessel when the vessel is being shaken. It may be dem¬ 
onstrated by placing a drop of any brilliant colored liquid, 
for which water has an affinity, into a vessel of quiet water, 
when the drop will be gradually diffused throughout the 
whole mass, showing not only that among the molecules of 
colored liquid there is activity, but that certain of the mole¬ 
cules before in the vessel plunge into and through the drop 
from all sides, dividing it into parts, and its parts again 
into other parts, until the particles are distributed through¬ 
out the mass. 

While the molecules are arranged in crystalline form, 
they require considerably more space than when in liquid 


164 WEIGHT, PRESSURE, AND MOTION OF WATER. 

form, and there are a less number of them in a cubic inch ; 
therefore a cubic inch of ice weighs less than a cubic inch 
of water. 

152. Relative Densities and Volumes.— The rela¬ 
tive changes in weight and volume of water at different 
temperatures are shown graphically in Fig. 8. When 


Fig. 8. 



weight is maintained constant and the temperature of the 
water is increased or decreased, the volume will change as 
indicated by the solid lines. When volume is maintained 
constant and the temperature increased or decreased, the 
weight will change as indicated by the dotted lines. 

WEIGHT OF WATER. 

153. Weight of Constituents of Water. —Water is 
substantially the result of the union (§ 150) of two volumes 
of hydrogen, having a specific gravity equal to 0.0689, and 
one volume of oxygen, having a specific gravity equal to 
1.102 ; but various other gases that come in contact with 
this combination are readily absorbed. 

Bulk for bulk, the oxygen is sixteen times heavier than 
the hydrogen. Water at its greatest density is about eight 
hundred and fifteen times as heavy as atmospheric air. 

The density of the vapor or gases enveloping the liquid 
molecules is greatest at a temperature of about 39°.2 Fall. 
At this temperature the greatest number of molecules is 








FORMULA FOR VOLUMES. 


165 


contained in one cubic inch, and the greatest weight for a 
given volume obtains. 

As the temperature of water rises from 39°.2, its gaseous 
elements expand and are supposed to increase their activity ; 
and a less number of molecules can be contained in a cubic 
inch, or other given volume; therefore the weight of water de¬ 
creases as the temperature rises from 39°.2 Fall. (vide Fig. 8.) 

154. Crystalline Forms of Water. —As the temper¬ 
ature falls below 39°.2 Fall., the molecules, under one at¬ 
mosphere of pressure, incline to arrange themselves in 
crystalline form, their action is supposed to be more vibra¬ 
tory and less progressive, and they become ice at a temper¬ 
ature of about 32° Fall. 

The relative weights and volumes of distilled water at 
different temperatures on the Fahrenheit scale are shown 
numerically in the table on the following page. 

Although there is a slight difference in the results of 
experiments of the best investigators in their attempts to 
obtain the temperature of water at its maximum density, it 
is commonly taken at 39.2° Fall., and the weight of a cubic 
foot of water at this temperature as 62.425 pounds, and the 
weight of a United States gallon of water at the same tem¬ 
perature as 8.379927 pounds. 

155. Formula for Volumes at Different Temper¬ 
atures.— The tables of weights and volumes of water is 
extended, with intervals of ten degrees, to the extreme limits 
within which hydraulic engineers have usually to experi¬ 
ment. The intermediate weights and volumes for inter¬ 
mediate temperatures, may be readily interpolated, or 
reference may be had to the following formulas taken from 
Watt’s “ Dictionary of Chemistry,” combining the law of 
expansion as determined by experiments of Mattliiessen, 
Sorby, Kopp, and Rossetti. 


166 


WEIGHT, PRESSURE, AND MOTION OF WATER. 


TABLE No. 38. 

Weight and Volume of Distilled Water at Different 

Temperatures. 


Temperature 

Fah. 

Weight of a cu. 
ft. in pounds. 

Difference. 

Ratio of volume to 
volume of equal wt. 
at max. density of 
temperature, 

39.2 0 Fah. 

Difference. 

Ice. 

57.200 

• • • • 

.916300 

• • • • 

3 2 ° 

62.417 

5-217 

I.OOOI29 

.083829 

39 - 2 ° 

62.425 

. 008 

I.OOOOOO 

.OOOI29 

40 ° 

62.423 

.002 

I.OOOOO4 

.OOOO04 

5 °° 

62.409 

.014 

I.OOO253 

.000249 

6o° 

62.367 

.042 

I.OOO929 

.000676 

7 o° 

62.302 

.065 

I.001981 

.OOIO52 

8o° 

62.218 

.084 

I.OO332 

.OOI339 

9 °° 

62.II9 

.099 

I.OO492 

.00160 

IOO° 

62.OOO 

.119 

I.00686 

.OO194 

I IO° 

6l.867 

•i 33 

I.00902 

.00216 

120° 

6l .720 

.147 

1 • 01r 43 

.00241 

1 3 °° 

61.556 

. 164 

1.01411 

.00268 

140° 

6l.388 

. 168 

1.01690 

.00279 

* 5 °° 

6l.204 

. 184 

1.01995 

• 00 3°5 

i6o° 

6l.007 

.197 

1.02324 

.00329 

170° 

60.80I 

. 206 

1.02671 

.00347 

180 0 

60.587 

. 214 

03033 

00362 

190° 

60.366 

. 221 

1.03411 

.00378 

200° 

60.136 

.230 

1.03807 

.00396 

210° 

59•894 

. 242 

1.04226 

.00419 

212° 

59-707 

, 187 

1.04312 

.00086 


Let V= ratio of a given volume of distilled water, at the 
temperature, T, on Fahrenheit’s scale, to the volume of an 
equal weight, at the temperature of maximum density. 

W= weight of a cubic foot of distilled water, in pounds, 
at any temperature, Fahrenheit. 

For temperatures 32° to 70° Fah. 

v— 1.00012 — 0.000033914 x (T — 32) + 0.000023822 x 
(T - 32)* - 0.000000006403 (T - 32) s . 























COMPRESSIBILITY AND ELASTICITY OF WATER. 167 


For temperatures above 70 \ 

Y = 0.99781 + 0.00006117 x (T - 32) + 0.000001059 x 
(T - 32) 2 . 


W= 


62.425 

v 


15G. Weight of Pond Water. — Fresli pond and 
brook waters are slightly heavier than distilled water, and 
when not loaded with sediment have, for a given volume, 
an increased weight equal to from 0.00005 to 0.0001 of an 
equal volume of distilled water. 

157. Compressibility and Elasticity of Water.— 
The compression of rain-water, according to experimental 
results of Canton, is 0.000046 and of sea-water 0.000040 of 
its volume under the pressure of one atmosphere. 

According to experiments of Regnault, water suffers a 
diminution of volume amounting to 48 parts in one million, 
when submitted to the pressure of one atmosphere, equal to 
14.75 pounds per square inch, and to 96 parts when sub¬ 
mitted to twice that pressure. 

Grassi found the compressibility of water to be 50 parts 
at 37° Fah., and 44 parts at 127° Fah. in each million 
parts, with one atmosphere pressure. 

A column of water 100 feet high would, according to 
these estimates, be compressed nearly one-sixteenth of an 
inch. 

The degree of elasticity of fluids was discovered by Can¬ 
ton in 1762. He proved that the volume of liquids dimin¬ 
ished slightly in bulk under pressure and proportionally 
to the pressure, and recovered their original volume when 
the pressure ceased. 

This has been confirmed by experiments of Sturm, 
CErsted, Regnault, and others. 



168 WEIGHT, PRESSURE, AND MOTION OF WATER. 

PRESSURE OF WATER. 

158. Weights of Individual Molecules.— If again 

we consider tlie molecules of water magnified, as before ex¬ 
plained, we can conceive that each molecule has its indi¬ 
vidual weight , and is subject , independently , to the force 
of gravity. Consider again the film of water of one-liun- 
dredth of an inch in depth, flowing through the orifice of 
same depth, and imagine the orifice to be magnified also in 
the same proportion as the molecules have been imagined 
to be magnified, that is, to five million molecule diameters; 
then the immense leverage that gravity has, proportionally, 
upon each molecule to set it in motion and to press it out 
of the orifice can be conceived, and the reason wdiy there is 
apparently so little frictional resistance to the passage of 
the molecules over each other will be apparent. 

159. Individual Molecular Actions. —The magnified 
molecule can also be conceived to be acting independently 
upon any side of its retaining vessel, or upon any other 
molecule, with which it is in contact, with the combined 
weight or pressure of all the molecules acting upon it. 

In a volume of fluid, each molecule presses in any 
direction from which a sufficient resistance is opposed , 
with a pressure due to the combined natural pressures of 
all molecules acting upon it in that direction , and also 
with the pressure transmitted through them from any 
exterior force. 

In treatises on hydrostatics, propositions relating to 
pressures of fluids are commonly stated in some form sim¬ 
ilar to the following :* “ When a fluid is pressed by its own 
weight, or by any other force, at any point it presses 
equally in all directions.” 


* Vide Hutton’s Mathematics, Hydrostatics, §310. 



INDIVIDUAL MOLECULAR REACTIONS. 


169 


160. Pressure Proportional to Depth.— The pres¬ 
sure of a fluid at any point on an immersed surface, is in 
pi oportion to tlic vertical depth, of that point Ibelow the sur¬ 
face of the fluid ; but not in proportion to variable breadths 
of the fluid. 

In vessels of shapes similar to Fig. 9 and Fig. 10, con¬ 
taining equal vertical depths of water, the pressures on 
equal areas of the horizontal bottoms are equal; also the 
pressures on equal and similar areas of their vertical sides, 
having their centres of gravity at equal depths, are equal. 


Fig. 9. Fig. 10. 



161. Individual Molecular Reactions. —Any parti¬ 
cle of fluid that receives a pressure reacts with a force equal 
to the pressure , if its motion is resisted upon the opposite side. 

Any point of a fixed surface pressed by a particle of 
water reacts upon the particle with a force equal to the 
pressure of the particle. 

The large body of water in the section A of the tank, 
Fig. 9, is perfectly counterbalanced by the slender body 
in the section a". A pressure equal to that due to the 
weight of all the particles above the horizontal bottom sur¬ 
face, /, acts upon that surface, and the surface reacts with an 
equal pressure and sustains all those particles. The effect 
would be similar if the surface, or a portion of it, was in¬ 
clined or curved ; therefore, only a pressure equal to the 



























170 WEIGHT, PRESSURE, AND MOTION OF WATER. 

weight of those particles vertically over the opening in the 
partition, /, acts upon the column below the partition f. 
Tire right and left horizontal pressures of the individual 
particles of A are transmitted to the particles on the right 
and left, which, in turn, react with equal pressures, and sus¬ 
tain them from motion sideways. The particles in contact 
with the partitions a and b transmit their pressures horizon¬ 
tally to the partition, which in turn react and sustain them, 
and all the particles remain in equilibrium. 

162. Equilibrium Destroyed by an Orifice. —If an 
orifice is made at the bottom of the side Z>, then the particles 
at that point will be relieved of the reaction of the point, or 
of its support, equilibrium will be destroyed, and motion 
will ensue, and all the particles throughout A will begin to 
move toward the orifice, though not with equal velocities. 

163. Pressures from Vertical, Inclined and Bent 
Columns of Water. —In Fig 10 the particles in the body 
of water, B , are pressed with a pressure due to the weight 
of any one vertical column of particles or molecules in the 
body of water above the opening in the partition g , conse¬ 
quently the reaction horizontally from any point in the 
partition c', or downward from any point in the covering 
partition g , or upward from any point in the bottom d, is 
equal to the weight of a column of molecules pressing upon 
that point, of height equal to the depth of the given point 
below the surface of the water ah'. The pressure due to 
this vertical column of molecules would still remain the 
same if the column a'g was inclined or bent, so long as the 
water surface remained in the level a b\ as is evident by 
inspection of the column b." 

Since the downward reaction from any point in the sur¬ 
face g is equal to the pressure of a column of molecules 
equal in height to a g , this reaction is added to the action 


PRESSURE UPON A UNIT OF SURFACE. 


171 


of gravity on all the molecules beneath the given point in g , 
therefore the pressure on any point in d , beneath the given 
point in g, is equal to the pressure of a column of molecules 
of height a d. 

1G4. Artificial Pressure. —If in the vessel illustrated 


by Fig. 10, we close the openings b' and b" at the level of 
the water surface, and tit a piston carrying a weight into 
the opening a', then we will increase the pressure at points 
d , g, c\ b\ b'\ etc., respectively, an amount equal to the 
pressure received by a point in contact with the piston at ct'. 
This artificial pressure is equal in effect to a column of fluid 
placed upon a’ of weight equal to the weight of the loaded 
piston. 

1G5. Pressure upon a Unit of Surface. —Since one 
cubic foot of water, measuring 144 square inches on its 
base and 12 inches in height weighs 62.425 pounds, there 
must be a pressure exerted by its full bottom area of 62.425 
pounds, and by each square inch of its bottom area of 


Z 62.425 lbs. 
\ 144 sq. in. 


0.433472 pounds for each foot of vertical 


depth of the water. 

In ordinary engineering calculations 62.5 pounds is 
taken as the weight of one cubic foot of water, and 0.434 
pounds as the resulting pressure per square inch for each 
vertical foot of depth below the surface of the water. These 
weights used in the computation of the following table, give 
closely approximate results, slightly in excess of the true 
weights. 

In nice calculations, as for instance, relating to tests of 
turbines to determine their useful effect, or of pumping 
engines to determine their duty, the weights due to the 
measured temperatures of the water are to be taken. 



172 WEIGHT, PRESSURE, AND MOTION OF WATER. 

TABLE No. 39. 


Pressures of Water at Stated Vertical Depths below the 
Surface of the Water, at Temp. 39. 2 0 Fah. 


Depth. 

Pressure per 
Sq. Inch. 

Pressure per 
Sq. Foot. 

Depth. 

Pressure per 
Sq. Inch. 

Pressure per 

Sq. Foot. 

Feet. 

Pounds. 

Pounds. 

Feet. 

Pounds. 

Pounds. 

I 

•4335 

62.425 

36 

15.60 

2247.30 

2 

.8670 

124.85 

37 

16.04 

2309.72 

3 

1 * 3 °° 

187.27 

38 

16.47 

2372.15 

4 

i -734 

248.70 

39 

16.91 

2434-57 

5 

2.167 

312.12 

40 

17-34 

2497.00 

6 

2.601 

374-55 

4 i 

17.77 

2 559-42 

7 

3-°35 

436.97 

42 

18.21 

2621.85 

8 

3.468 

499.40 

43 

18.64 

2684.27 

9 

3.902 

561.82 

44 

19.07 

2746.70 

10 

4-335 

624.25 

45 

T 9 - 5 1 

2809.12 

11 

4.768 

686.67 

46 

19.94 

2871.55 

12 

5.202 

749.10 

47 

20.37 

2933-97 

13 

5*636 

811.52 

48 

20.81 

2996.40 

14 

6.069 

873-95 

49 

21.24 

3058.82 

15 

6 - 5°3 

936-37 

5 ° 

21.67 

3121.25 

16 

6.936 

998.80 

60 

26.01 

3745-5 

17 

7 - 37 o 

1061.23 

70 

30-35 

437 o 

18 

7.803 

1123.65 

80 

34.68 

4994 

19 

8.237 

1186.07 

90 

39 - 01 

5618 

20 

8.670 

1248.50 

100 

43-35 

6242.5 

21 

9.104 

1310.92 

no 

47.68 

6867 

22 

9-537 

1 37 3-35 

120 

52.02 

749 1 

2 3 

9.971 

1435-77 

130 

56.36 

8115 

24 

IO.4O 

1498.20 

140 

60.69 

8739 

2 5 

IO.84 

1560.62 

45 ° 

65- 0 3 

9364 

26 

11.27 

1623.05 

160 

69.36 

9988 

27 

11.70 

1685.47 

170 

73-70 

10612 

28 

12.14 

•1747.90 

180 

78.03 

11237 

29 

I2 -57 

1810.32 

190 

82.36 

11861 

30 

13.00 

1872.75 

200 

86.70 

12485 

3 i 

13-44 

1 935 * 1 7 

210 

91.04 

I 3 I °9 

3 2 

i 3- 8 7 

1997.60 

220 

95-37 

1 37 33 

33 

14-31 

2060.02 

230 

99.71 

1435 8 

34 

H -74 

2122.45 

240 

IO4.O4 

14982 

35 

I 5- I 7 

! 

2184.87 

2 5 ° 

108.37 

15606 


160. Equivalent Forces. —In many computations in 
elementary statics we are accustomed to consider the force 


























A LINE A MEASURE OF WEIGHT. 


173 


acting from a weight as equivalent to tlie force of a pressure 
and to place weights to represent statical forces. 

On one square foot of the bottom of a vessel containing 
one foot depth of water, a pressure is exerted by the water 
that would tend to prevent any other force from lifting up 
that bottom. We might remove that water and substitute 
the pressure of a quantity of oil, or of stone, or of iron, as 
an equivalent for the pressure of the water, but to be an 
exact equivalent its weight must be exactly the same as the 
weight of the water. In this case we should take for the 
62.5 pounds pressure in the water, 62.5 pounds weight of 
oil, or of stone, or of iron. 

167. Weight a Measure of Pressure. —Weight is, 
then, a standard whose unit is one pound, by which pres¬ 
sures may be compared and measured. 


Fig. 11. 



/ 


168. A Line a Measure of Weight. —In graphical 
statics we are also accustomed to represent weights by lines 
which are drawn to some scale. 

If two forces act upon the centre of gravity of a body, 
Fig. 11, one of which, a, is equal to 30 pounds, and the 
other b, to 40 pounds, we can, after adopting some scale, 













174 WEIGHT, PRESSURE, AND MOTION OF WATER. 

say one inch, to equal one pound, represent the force a by 
a line 30 inches long, drawn from some given point, g, in its 
direction of action, ga', and the force b by a line 40 inches 
long, drawn from the same point, in its direction, gb\ Now, 
if we draw lines from the end of each line thus produced 
parallel to the other line to r, completing the parallelogram, 
and then draw the diagonal, gr , then tiie resultant of the 
two forces will pass through the line gr , and the length of 

gr will represent the combined effect of the two forces in 

• ____ 

this direction. Its length will be 50 inches = Vigb 1 ) 2 + {b'r) 2 , 
and the combined effect of the two forces in this direction 
will be 50 pounds. 

169. A Line a Measure of Pressure upon a Sur¬ 
face. —Let the dimensions of the top surface of the body A, 
be 10 feet long and 3 feet wide, and its area be 30 square 
feet; let the side dimensions, B, be 10 feet long and 4 feet 
high, and its area be 40 square feet; let the pressure upon 
each surface be one pound per square foot, and the direc¬ 
tion of the pressure be shown by the arrows a and b. The 
body being solid, the forces are to be considered as acting 
through its centre of gravity. We can now plot the pres¬ 
sure upon A of 30 pounds in its direction, and upon B of 
40 pounds in its direction, and the diagonal of the parallel¬ 
ogram gr will give the direction and ratio of the resultant, 
as before. The forces being equal to those before considered 
as acting upon a point, will again give a diagonal 50 inches 
long and indicating an elfect of 50 pounds. 

It is plain, then, that we can take the line ga\ or the 
line b'r, which is equal to it, to represent the force or pres¬ 
sure a acting upon the point g or upon the surface A ; and 
we can take the line gb\ or the line aV, to represent the 
force or pressure b acting upon the point g or the surface B , 
and the line gr to represent the combined effect of the two 



ANGULAR RESULTANT OF A FORCE 


175 


forces. In various calculations it is convenient to Ibe able 
to do this. 

170. Diagonal Force of Combined Pressures 
Graphically Represented. —Again, if we know the mag¬ 
nitude of the force r acting through the centre of the body, 
and we desire to know the magnitude of the effects upon 
the sides A and B, in directions at right angles to them, 
that produced the force r, we draw the line r to a scale in 
the direction the force acts, and from both of its ends draw 
lines to the same scale in directions at right angles to the 
sides A and B , and proportional to their areas, as ga' and gb', 
and complete the parallelogram ; then will ga' measured to 
scale indicate the effect of the force a upon A, and gb’ 
measured to scale indicate the force b upon B. If gr 
measures 50 pounds, then will ga' measure 30 pounds and 
gb' measure 40 pounds. 

171. Angular Resultant of a Force Graphically 
Represented. —If a force represented by the line ag, 
Fig. 12, acts upon and at right 
angles to an inclined surface fe 
at g, then its horizontal resultant 
will be represented by the line 
5*7, and the end b w T ill be perpen¬ 
dicularly beneath a. The ratios 
of the lengths of the lines ag and 
ab and bg are the ratios of the 
effects of the force in their three 
directions respectively. 

If a perpendicular line be let fall from / upon the hori¬ 
zontal line ed , intersecting it in d, then the ratio of fe to fd 
will be equal to the ratio of ag to bg ; consequently, the 
horizontal pressure or effect of the force ag upon fe would 
be to its direct effect as fd is to fe. Therefore, the ratio of 


Fig. 12. 






176 


WEIGHT, PRESSURE, AND MOTION OF WATER. 


the line fd to fe equals the ratio of tlie horizontal effect of 
the direct force upon fe. 

The ratio of the vertical downward effect of the force a 
upon fe is to its direct effect as the length ab to the length 
cup and also as the length ed to the length ef. Therefore, 
the ratio of the line or surface ed to the line fe represents 
the ratio of the vertical downward effect of the direct force 
upon fe. 

17 2 . Angular Effects of a Force Represented by 
the Sine and Cosine of the Angle. —Also, ab is the 
sine, and bg the cosine of the angle agn, and we have seen 
that their ratios are to radius ag as ed and fd are to fe; 
therefore the vertical and horizontal effects of the force a 
upon the inclined surface fe are to its direct force as the sine 
and cosine of the angle efd is to radius fe. 

173. Total Pressure. —To find the toted pressure of 
quiet water on any given surface: Multiply together , its 
area , in square feet; the vertical depth of its centre of 
gravity , below the water surface, in feet; and the weight 

of one cubic foot of water 
in pounds (= 62.5 lbs.). 

In the tank, Fig. 13, 
filled with water, let the 
depth ab be 9 feet; then 
the centre of gravity of 
the surface ab will be at 
a depth from a equal to 
one-half ab = 4J feet. If 
the length of the side ab 
is 1 foot, then the total pressure on ab will equal 

9 ft. x 1 ft. x 4£ ft. x 62.5 lbs. = 2531.25 lbs. 

174. Direction of Maximum Effect.— The direction 
of the maximum eff'ect of a pressure on a plane surface is 


Fig. 13. 










CENTRES OF PRESSURE AND OF GRAVITY. 177 

always at right angles to the surface. The maximum hori¬ 
zontal effect of the pressure on the unit of length of ab 
equals the product of ab, into the depth of its centre of 
gravity, into the unit of pressure. The horizontal effect of 
pressure on the unit of length of cd equals the product of 
its vertical projection ce, into the depth of its centre of 
gravity, into the unit of pressure ; and the vertical effect of 
pressure on cd equals the product of its horizontal projec¬ 
tion de, into the depth of its centre of gravity, into the unit 
of pressure. 

175. Horizontal and Vertical Effects. —Assuming 
the length of the side cd to be radius of the angle dee, then 
the total pressure on cd is to its horizontal effect as radius 
cd is to the cosine ce of the angle dee , or as the surface cd 
is to its vertical projection ce / and the total pressure is to 
its vertical effect as radius cd is to the sine de of the same 
angle, or as cd to de. 

The total pressure on dg is to its horizontal effect as dg 
is to fg, or to the cosine of the angle dgf; and to its vertical 
effect as dg to df , or to the sine of the angle dgf. 

116. Centers of Pressure and of Gravity. —The 
centre of hydrostatic pressure , which tends to overturn or 
push horizontally the surface of equal width, ab , is not in 
the center of gravity of that surface, but in a point at tu r o- 
thirds the depth from a at p = 6 feet. 

The center of gravity of the surface cd is at one-half the 
vertical depth ce, at li, or at one-half the length of the slope 
cd , at h. The points h and h' are both in the same hori¬ 
zontal plane. When the water surface is at ac, the center 
of pressure of the surface cd is at two-thirds of the vertical 
depth ce , at p ', or at two-thirds the slope cd , at p. The 
points p' and p are in the same horizontal plane. If ce 
equals six feet, then the center of gravity of cd or ce will be 
12 


178 


WEIGHT, PRESSURE, AND MOTION OF WATER. 


at tlie vertical depth of three feet = ch\ and the center of 
pressure at the vertical depth of four feet — cp. 

The center of gravity of the surface dg is at a depth 
from the water surface c, equal to the sum of one-lialf the 

fn 

vertical depth fg added to the depth ce — ce and the 


center of pressure of dg is at a vertical depth equal to 


2 ( cg'f — ( ce) 

3 (eg? - (ce) 


- = cp"- 7.6 feet. 


177. Fissure upon a Curved Surface and Effect 
upon to Projected Plane. —In a vessel, Fig. 14, filled 
with water, one of whose ends, ab , is a segment of a cylin¬ 
der, and opposite end in 
part of the vertical plane 
a'b", and in part of a 
hemisphere cd, the total 
pressure on ab will be 
as the total surface ab; 
but its horizontal effect 
will be as the area of its 
vertical projection a'b'. The total pressure on the end a"b'\ 
will be as the remaining surface of the vertical plane a'b" 
increased by the concave surface of the hemisphere ckd, but 
its horizontal effect will be equal to its vertical projection 
a"'b"' or a'b'. The vertical effect on 
the plane a'b" is equal to zero, but 
the vertical effect of the pressure in 
the hemisphere is represented by 
the plan of one-half a sphere of 
diameter equal to cd. 

In a hollow sphere, Fig. 15, filled 
with water, the total pressure will 
be as the total concave surface ahbli ", but the horizontal 


Fig. 15. 





Fig. 14. 
















FLOATING AND SUBMERGED BODIES. 


179 


effect will be as its vertical projection ab , which represents 
a circular vertical plane of diameter equal to ab , and the 
vertical effect will be as its horizontal projection bb'\ which 
represents a horizontal circular area of diameter equal 
to bb 

In a pipe, or cylinder, represented also in section by 
Fig. 15, the total pressure within is as the inner circumfer¬ 
ential area a'7ib'7i", and when the cylinder lies horizontally 
the horizontal and vertical effects of its pressure in a unit 
of length will be represented by its vertical and horizontal 
projections ab and bb". 

If the cylinder is inclined, the pressure at any point 
upon its circumference is as the depth of that point below 
the surface of the water, and the total pressure in pounds 
upon any section of the cylinder will be found by multi¬ 
plying its area in square feet into the depth of its center of 
gravity, in feet, below the surface of the water and their 
product into the weight, in pounds (62.5 lbs.), of a cubic 
foot of water. 

178. Center of Pressure upon a Circular Area.— 

The center of pressure of a vertical circular area, repre¬ 
sented also by Fig. 15, when its top a is in the water surface, 
is at a depth below a equal to five-fourths the radius of the 
circle. 

179. Combined Pressures. —The sum of pressures in 
pounds, upon a number of adjacent surfaces, may be found 
by multiplying the sum of their surfaces in square feet into 
the depth of their common center of gravity, in feet, below 
the surface of the water, and this product into the weight of 
one cubic foot of water, in pounds (62.5 lbs.). 

180. Sustaining* Pressure upon Floating and 
Submerged Bodies. —The pressure tending to sustain a 
cylinder floating vertically in water c (Fig. 16) is equal to 


180 


WEIGHT, PRESSURE, AND MOTION OF WATER. 


Fig. 10. 


Fig. 17, 



a 


i 


I 


1 


1 

: 


X 

5 

' 

L 

* 


x 



£ 

■ 


x\ 

^wVxWVxwWV"' 

Os 


/ 


' V, .'WWWVVWAWV T1 


tlie vertical effect of the pressure on its bottom area. The 
sustaining pressure may be computed, in pounds, by mul¬ 
tiplying the bottom area of the cylinder, in square feet, into 
its depth, in feet (which gives the cubical contents of the 
immersed portion of the cylinder), and this product into 
the weight of a cubic foot of water. 

The weight of water displaced may be computed also by 
multiplying the cubic contents of the immersed portion of 
the cylinder, in cubic feet, into the weight of a cubic foot 
of water. The two results will be equal to each other ; 
therefore the vertical effect tending to sustain the cylinder 
is equal to the weight of water displaced. 

To compute the pressure tending to sustain the trun¬ 
cated cone, or pyramid, d , multiply the vertical projection 
of the inclined surfaces (= top area — bottom area), in feet, 
into the depth of their common center of gravity, in feet, 
and to this product add the product of its bottom area, in 
feet, into its depth, in feet, and then multiply the sum of 
the products into the weight of a cubic foot of water, in 
pounds. 

This sustaining pressure will also equal the weight of 
the water displaced. 

To compute the pressure tending to sustain the im¬ 
mersed cube e , multiply, in terms as before, the bottom 







































UPWARD PRESSURE UPON A SUBMERGED LINTEL. 181 


area into the depth and into the weight of water, and from 
the final product subtract the product of the top area into 
its depth and into the weight of water. This sustaining 
pressure also equals the weight of water displaced. 

The downward pressure on the top of e tends to sink it, 
and the upward pressure on its bottom to sustain it. The 
difference of the two effects is the resultant. The resultant 
will act vertically through the center of gravity of the body. 
If e is of the same specific gravity as the water, then its 
weight will just balance the resultant, and it will neither 
rise or fall; if of less specific gravity it will rise; if of 
greater, it will sink. The cylinder c is evidently of less 
specific gravity than the water, and d of the same specific 
gravity. 

Let c be a hollow cylinder with a water-tight bottom, 
then although it may be made of iron, and weights be 
placed within it, it will still float if its total weight, includ¬ 
ing its load, is less than the weight of the water it displaces. 
On the same principle iron ships float and sustain heavy 
cargoes. 

181. Upward Pressure upon a Submerged Lin¬ 
tel. —If L , Fig. 17, be a horizontal lintel covering a sluice 
between two reservoirs, the upward pressure of the water 
upon ij, tending to lift it, will be equal to the product of 
the rectangular area ij into its depth and into the weight 
of a cubic foot of water; that is, the upward pressure in 
pounds will be equal to the weight in pounds ot a prism 
of water having the rectangular area ij for its base and the 
depth of ij below the surface of the water for its height. 

If the lintel is constructed of timber, at a considerable 
depth, and is not equally as strong as the enclosing walls 
of the reservoir at the same depth, it may be broken in or 
thrust upward. 


182 WEIGHT, PRESSURE, AND MOTION OF WATER. 


Fig. 18. 


18*2. Atmospheric Pressure. —Upon the particles of 
all bodies of water resting in open vessels or reservoirs, 

there is a force constantly 
acting, in addition to the 
direct force of gravity, upon 
the independent particles. 
This force conies from the* 
effect of gravity upon the 
atmosphere. The weight 
of the atmosphere produces 
a pressure upon the sur¬ 
face of the water of about 
14.75 pounds per square 
inch, or about 2124 pounds per square foot. This is equiv- 

alent to a column of water (0 4334 72 = ) ^4.028 feet high. 



In the open vessel, Fig. 18, filled with water to the level 
a, the effect of the pressure of the atmosphere is transmitted 
through the particles, and acts on all the interior surface 
below the water surface abb a', with a force of 14.75 pounds 
on every square inch, in addition to the pressure from the 
weight of the water. There is also an equal atmospheric 
pressure on the exterior of the vessel of 14.75 pounds per 
square inch ; therefore the resultant is zero, and the weight 
of the atmosphere does not tend to move either side of the 
vessel or to tear the vessel asunder. 

183. Rise of Water into a Vacuum. —If the tube cd 
be extended to a height of thirty-five or more feet above the 
surface of the water, and a piston, containing a proper valve, 
be closely fitted in its upper end, then by means of the piston 
the air may be pumped out of the tube, and the surface of 
water in the tube relieved of atmospheric pressure. The 
equilibrium of the particles within the tube will then be de- 





























TRANSMISSION OF PRESSURE TO A DISTANCE. 183 

stioyed, and the pressure of the atmosphere acting through 
the particles in the lower end of the tube will press the 
■watei up the tube to a height, according to the perfection 
ol the vacuum, of 34.028 feet approximately. It is atmos¬ 
pheric pressure that causes pump cylinders to fill when they 
are above the free surface of the water. 

If the bottom of the immersed tube, cd , be closed by a 
valve, and the tube filled with water, and the top then 
sealed at a height of thirty-five or more feet above the sur¬ 
face of the water aa\ the valve at d may afterwards be 
opened, and the pressure of the atmosphere acting through 
the particles in the lower end of the tube will sustain the 
column to a height of 34.028 feet approximately. 

184. Siphon. —If the bent tube or siphon, efg , Fig. 18, 
having its leg /'g longer, vertically, than its leg c/, be filled 
with water and its end e inserted in th*e water A , then the 
action of gravity upon the water in the leg f g, will be 
greater than upon the water in the leg ef, and the equi¬ 
librium in the particles at f will be destroyed. The pres¬ 
sure of the atmosphere on the surface aa ', will constantly 
press the water A up the leg ef \ tending to restore the equi¬ 
librium, and gravity acting in the leg f g will as constantly 
tend to destroy the equilibrium, consequently there will be 
a constant flow of the water A out of the end g , until the 
water surface falls nearly to the level e, or until the air can 
enter at e. 

185. Transmission of Pressure to a Distance.— 

The effect of pressure on a fluid is transmitted through its 
particles to any distance , however indefinitely great , to the 
limit of its volume. 

If water is poured into the open top b", Fig. 10, the divi¬ 
sion b'c", will fill as fast as the division b", and the water 
will flow over b'g , and will reach the level a\ at approxi- 


184 WEIGHT, PRESSURE, AND MOTION OF WATER. 

mately the same time as it reaches b "; so in any inverted 
siphon, or in a system of water pipes of a town, water will 
in consequence of transmitted pressure, flow from an ele¬ 
vated source down through a valley and up on an opposite 
hill to the level of the source. If the syphon, or pipe, has 
an indefinite number of branches with open tops as high as 
the source, then the surface of the water at the source and 
in each of the branches will rest in the same relative eleva¬ 
tion of the earth’s curvature. 

18G. Inverted Siphon. —By transmission of pressure 
through the particles, water in a pool or lake near the sum¬ 
mit of one hill or mountain is sometimes, when the rock 
strata have been bent into a favoring shape, forced through 
a natural subterranean inverted siphon, and caused to flow 
out as a spring on an opposite hill or mountain summit, 

187. Pressure ‘Convertible Into Motion. —Thus we 
see that the force of gravity in the form of weight is con¬ 
vertible into pressure, and pressure into motion; and that 
motion may be converted into pressure, and pressure be 
equivalent to weight. 

Motion we are accustomed to measure by its rate, which 
we term its velocity ; that is, the number of units of space 
passed over by the moving body in a unit of time, as, feet 
per second. 

MOTION OF WATER. 

188. Flow of Water .—All forces tending to destroy 
equilibrium among the particles of a body of water tend 
to produce motion in that body. 

We have above referred to the accepted theory of motion 
due to the influence of caloric ; there is a motion of water 
due to the winds, a motion due to the attraction of the 
heavenly bodies, and an artificial motion, as, for instance, 


ACCELERATION OF MOTION. 


185 


that due to the pressure of a pump-piston. The motion 
herein to be considered is that originated by the influence 
of gravity and termed the flow of water. 

189. Action of Gravity upon Individual Mole¬ 
cules. — All natural flow of water is due to the force of 
gravity , acting upon and generating motion in its indi¬ 
vidual molecules. 

If in the side of a vessel filled with water there be made 
an orifice; if one end of a level pipe filled with water be 
lowered ; or if a channel filled with water have its water 
released at one end, then equilibrium among the particles 
of the water will be destroyed, and motion of the water will 
ensue. Gravity is the force producing motion in either case, 
and it acts upon each individual molecule as it acts upon a 
solid body, free to move, or devoid of friction. 

190. Frictionless Movement of Molecules. — The 
molecules of water move over and past each other with such 
remarkable ease that they have usually been considered as 
devoid of friction. 

The formulas in common use for computing the velocity 
with which water flows from an orifice in the bottom or side 
of a tank filled with water, assume that the individual 
molecules, at the axis of the jet, will issue with a velocity 
equal to that the same molecules would have acquired if 
they had fallen freely, in vacuo, in obedience to gravity, from 
a height above the orifice equal to the height of the surface 
of the water. 

191. Acceleration of Motion. —The force of gravity 
perpetually gives new impulse to a falling body and accel¬ 
erates its motion , if unresisted, in regular mathematical 
proportion. 

Experiment has shown that a solid body falling freely 
in vacuo , at the level of the sea, passes through a space or 


186 WEIGHT, PRESSURE, AND MOTION OF WATER. 

height of 16.1 feet nearly, during the first second of time; 
has a velocity at the end of the first second of 32.2 feet 
nearly, and is accelerated in each succeeding second 32.2 
feet nearly. The usual symbol of this rate of acceleration 
is g, the initial of the word gravity, and we shall have fre¬ 
quent occasion for its use. 

The latitude and altitude, or distance from the centre of 
the earth, affects the rate of motion slightly, but does not 
affect materially the results of ordinary hydrodynamic cal¬ 
culations. 

The resistance of the air affects slightly the motion of 
dense bodies, and retards them more if they are just sepa¬ 
rating, as water separates into spray. 

192. Equations of Motion. —The velocity, v , acquired 
by a solid body at the end of any time, t , equals the prod¬ 
uct of time into its acceleration by gravity, g, and is directly 
proportional to the time : 

v : g :: t : 1, or v = gt. 

The height, h , through which the body falls in one 
second of time equals \g, and the heights in any given 
times, t , are as the squares of those times : 

h : \g :: t 2 : (l) 2 , or h - \gt 2 ; 
and, by transposition, we have 



This value of t in the equation of v gives 



From these equations we deduce the following general 
equations of time, t; height , h; velocity , v; and accelera¬ 
tion , g: 


PARABOLIC PATH OF THE JET. 

187 

t = v 

g 

II 

1 

II 

= .031063/) 

a) 

n - 2 

II 

^ l(M 

II 

~ = .015536®* 

(2) 

» = gt 

II 

II 

V2 gh = 8.0227 Vh 

(3) 

53 -to 

II 

ii 

Ioj 

II 

A = 32.1908 

2 h 

(4) 


The time, space, and velocity are at the ends of the first 
ten seconds as follows : 


Time (t) . 

1 

2 

3 

4 

5 

6 

7 

8 

9 

IO 

Space (A) . 

Velocity (v) . 

16.1 

64.4 

144.9 

257.6 

402.5 

579 6 

788.9 

1030.4 

1304.1 

1600 

32.2 

64.4 

96.6 

128.8 

161.0 

193.2 

225.4 

257.6 

289.8 

322 

Acceleration (§) . 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 

32.2 


193. Parabolic Path of the Jet. —If we plot the 


spaces of the column of 
spaces or heights to a 
scale on a vertical line, 
beginning with zero at 
the top, and then from 
the space points plot 
horizontally to scale the 
velocities, as in Fig. 19, 
and then from zero draw 
a curved line ac , cutting 
the extremities of the 
horizontal lines, the 
curve ac will be a pa¬ 
rabola, the vertical line 
ab its abscissa, and the 
horizontal lines its ordi¬ 
nates. 


c c/3 

.5-0 

03 C 

p ° 
g o 

fc -1 C/3 


rj -W 
§.8 


Fig. 19. 


E .S Velocity in feet per second, 

a 





























188 WEIGHT, PRESSURE, AND MOTION OF WATER. 

194. Velocity of Efflux Proportional to the Head., 

—If in the several sides of a reservoir A, Fig. 19a, kept 
filled with water, orifices with thin edges are made at 
depths of 20 feet, 25 feet, 50 feet, 75 feet, and 100 feet from 
the surface of the water, then water will issue from each 


Fig. 19 a . 



orifice in a direction perpendicular to the side, with a veloc¬ 
ity proportional to the square root of the head of water 
above the centre of gravity of the orifice, and equal approx¬ 
imately to the velocity one of its particles would have 
acquired if it had fallen freely from the height of the head. 

195. Conversion of the Force of Gravity from 
Pressure into Motion. —The accumulated vertical force 
of gravity due to the head or “ charge” will act upon the 





















EQUAL PRESSURES GIVE EQUAL VELOCITIES. 


189 


particles as pressure before the orifice is opened, but in¬ 
stantly upon an orifice being opened pressure will impel 
the particles, of water in the direction of the axis of the 
orifice, and gravity will begin anew to act upon the parti¬ 
cles in a vertical direction. If the axis of the orifice is not 
vertical, gravity will deflect the particles through a curved 
path. 

196. Resultant Effects of Pressure and Gravity 
upon the Motion of a Jet. —If on a line at, drawn 
through the center of an orifice, perpendicular to the plane 
of the orifice, we plot to scale the products of any given 
times into a given velocity, and from each of the points 
thus indicated we plot vertically downward the distance, a 
body will fall freely in those times, op, and then from the 
orifice draw a line through the extremities of the vertical 
lines, the curved line thus sketched will indicate the path 
of the jet flowing from the orifice. The curved line is a 
parabola, to which the axis of the orifice is tangent; and 
the distances ao upon the tangent are equal and parallel to 
ordinates, and represent the force per unit of time given to 
the particles of the jet by pressure, and the verticals from 
the tangent are equal and parallel to abscisses, and repre¬ 
sent by their increase the accelerating effect of gravity upon 
the falling particles. The distances ao and op, ordinates ap, 
and abscisses ad, form a series of parallelograms, one angle 
of which lies in the orifice and the opposite angles of which 
lie in the curved path of the jet, and the diagonals of which 
are equal to resultants of the effects of pressure and gravity. 

197. Equal Pressures give Equal Velocities in all 
Directions. —The velocities of issues, downward from the 
orifice c and upward from the orifice c, and horizontally 
from the lower orifice b', will be equal, since they all are at 
the same depth. 


190 WEIGHT, PRESSURE, AND MOTION OF WATER. 

198. Resistance of the Air. —Since the velocity of 
upward issue from c is due to the gravity force of the head 
dc , acting as pressure, the jet should theoretically reach the 
level of the water surface d. The spreading of the particles 
and consequent enhanced resistance of the air prevents such 
result, and the resistance increases as the ratio of area of 
orifice to height of head decreases. 

199. Theoretical Velocities. —The following table of 
theoretical velocities and times due to given heights or heads 
has been prepared to facilitate calculation : 

TABLE No. 40. 

Correspondent Heights, Velocities, and Times of Falling 

Bodies. 


II 

V = Y 2§H 

«s. 

11 

< 

He! 

II 

£ 1 1:3 

1 

1 

V = 



Head in feet. 

Velocity in feet 
per second. 

Time 

in seconds. 

Head in feet. 

Velocity in feet 
per second. 

Time 

in seconds. 

.OIO 

.80 

.0248 

•145 

3 

05 

.0949 

.015 

.98 

.0304 

.150 

3 

II 

.0964 

.020 

I * I 3 

.0350 

•155 

3 

l6 

.O9S0 

.025 

1.27 

•0394 

. 160 

3 

21 

•0995 

.030 

1-39 

.0431 

.165 

3 

26 

. IOII 

•035 

1.50 

.0465 

.170 

3 

31 

. IOl6 

.040 

1.60 

.0496 

•175 

3 

36 

. IO42 

•045 

1.70 

.0527 

.1S0 

3 

40 

• io 54 

.050 

1.79 

•0555 

.185 

3 

45 

. 1069 

.055 

1.88 

•0583 

. 190 

3 

50 

.1085 

.060 

1.97 

.0611 

•195 

3 

55 

.1100 

.065 

2.04 

.0632 

.20 

3 

59 

.1113 

.070 

2.12 

.0657 

.21 

3 

68 

.1141 

•075 

2.20 

.0682 

.22 

3 

76 

.1166 

.0S0 

2.27 

.0704 

•23 

3 

85 

•1193 

.085 

2-34 

.0725 

.24 

3 

93 

. 1221 

.090 

2.41 

.0747 

•25 

4 

01 

.1243 

•095 

2.47 

.0766 

.26 

4 

09 

.1268 

.100 

2.54 

.0787 

.27 

4 

17 

.1293 

.105 

2.60 

.0S06 

.28 

4 

25 

•1317 

.110 

2.66 

.0825 

.29 

4 

32 

•1339 

•115 

2.72 

.0843 

•30 

4 

39 

.1361 

. 120 

2.78 

.0862 

•3i 

4 

47 

.1386 

.125 

2.84 

.0880 

•32 

4 

54 

.1407 

.130 

2.89 

.0896 

•33 

4 

61 

. 1429 

•135 

2-95 

.0914 

•34 

4 

68 

•1451 

.140 

3.00 

.0930 

•35 

4 

75 

.1472 






























THEORETICAL VELOCITIES. 


191 


Correspondent Heights, Velocities, and Times of Falling 

Bodi es—( Continued .) 


H = — 

2 g 

= 4'2^'H 

■V? 

\\x 

11 

X 

V = 4 / 2^H 

•v? 

Head in feet. 

Velocity in feet 
per second. 

Time 

in seconds. 

Head in feet. 

Velocity in feet 
per second. 

Time 

in seconds. 

•36 

4.81 

.1491 

•83 

7-31 

.2266 

•37 

4.87 

.1510 

.84 

7-35 

.2278 

•33 

4.94 

.1531 

•85 

7.40 

. 2294 

•39 

5.OI 

•1553 

.86 

7-44 

. 2306 

.40 

5-07 

.1572 

.87 

7.48 

.2319 

.41 

5-14 

•1593 

. 88 

7-53 

•2334 

.42 

5.20 

. 1612 

. 89 

7-57 

•2347 

•43 

5.26 

.1634 

.90 

7.61 

•2359 

•44 

5-32 

. 1649 

.91 

7-65 

•2377 

•45 

5.38 

.1668 

.92 

7.70 

.2387 

.46 

5-44 

. 1686 

•93 

7-74 

•2399 

•47 

5-50 

•1705 

•94 

7.78 

.2412 

.48 

5-56 

.1724 

•95 

7.82 

.2424 

•49 

5-62 

.1742 

.96 

7.86 

•2437 

•50 

5-67 

•1758 

•97 

7.90 

•2449 

• 5 i 

5-73 

.1779 

.98 

7-94 

.2461 

•52 

5-79 

•1795 

•99 

7.98 

.2474 

•53 

5.35 

.1813 

1. 

8.03 

• 249 1 

•54 

5 - 9 ° 

. 1829 

1.02 

8.10 

.2518 

••55 

5-95 

.1844 

1.04 

8.18 

•2543 

•56 

6.00 

. i860 

1.06 

8.26 

.2567 

•57 

6.06 

.1879 

1.08 

8-34 

.2589 

•53 

6.11 

. 1894 

1.10 

8.41 

.2616 

•59 

6.17 

• I 9 I 3 

1.12 

8.49 

.2638 

.60 

6.22 

. 1928 

1.14 

8-57 

. 2660 

.61 

6.28 

.1947 

1.16 

8.64 

.2685 

.62 

6.32 

•1959 

1.18 

8.72 

.2706 

•63 

6-37 

•1975 

1.20 

8-79 

.2730 

.64 

6.42 

. 1990 

1.22 

8.87 

•2751 

•65 

6.47 

.1999 

1.24 

8.94 

•2774 

.66 

6.52 

.2021 

1.26 

9.01 

•2797 

.67 

6-57 

•2037 

1.28 

9.08 

.2819 

.63 

6.61 

.2049 

1.30 

9- 1 5 

.2842 

.69 

6.66 

.2065 

1.32 

9.21 

.2866 

.70 

6.71 

.2080 

1-34 

9.29 

.2885 

• 7 i 

6.76 

.2096 

1.36 

9-36 

.2906 

.72 

6.81 

.2111 

1.38 

9-43 

.2927 

•73 

6.86 

.2127 

1.40 

9-49 

.2950 

•74 

6.91 

.2142 

1.42 

9-57 

. 2968 

•75 

6.95 

• 2154 

1.44 

9- 6 3 

.299I 

.76 

6.99 

.2167 

1.46 

9.70 

.3010 

•77 

7.04 

.2182 

1.48 

9-77 

.3030 

.78 

7.09 

.2198 

1.50 

9- 8 3 

•3052 

•79 

7-13 

.2210 

i -55 

9.98 

.3106 

.80 

7.18 

.2226 

1.60 

10.2 

•3137 

.81 

7.22 

.2238 

1.65 

10.3 

.3204 

.82 

7.26 

.2251 

1.70 

10.5 

•3238 

































192 WEIGHT, PRESSURE, AND MOTION OF WATERS. 

Correspondent Heights, Velocities, and Times of Falling 

Bodies—( Conti?iued .) 


H = — 

V = F 2^H 

-v? 

h=t! 

2<r 

v = y 2gn 

II 

•'ISil 

HmH in fppf- 

Velocity in feel 

Time 

Hfiflri in fnnt 

Velocity in feel 

Time 


per second. 

in seconds. 


per second. 

in seconds. 

1.75 

10.6 

.3302 

8.4 

23-3 

.7210 

1.80 

10.8 

•3333 

8.6 

23-5 

.7319 

1.85 

10.9 

•3394 

8.8 

23.8 

•7395 

1.90 

11.1 

•3423 

9 - 

24.1 

.7469 

1-95 

11.2 

.3482 

9.2 

24-3 

•7572 

2. 

11.4 

•3509 

9.4 

24.6 

.7642 

2.1 

11 -7 

•3590 

9.6 

24.8 

•7742 

2.2 

11.9 

•3697 

9.8 

25.1 

. 7809 

2-3 

12.2 

•3770 

10. 

25-4 

.7866 

2.4 

12.4 

•3871 

10.5 

26. 

•8077 

2-5 

12.6 

.3968 

11. 

26.6 

•8277 

2.6 

12.9 

.4031 

11 • 5 

27.2 

.8456 

2.7 

13.2 

.4091 

12. 

27.8 

•8633 

2.8 

13-4 

.4179 

12.5 

28.4 

. 8803 

2.9 

13-7 

•4234 

13 - 

28.9 

.8997 

3 - 

13-9 

•4317 

13-5 

2 9-5 

•9153 

3 -i 

14.1 

•4397 

14 - 

30 . 

•9333 

3-2 

14-3 

.4476 

14-5 

30.5 

• 9508 

3-3 

14-5 

•4552 

15 - 

3i.1 

.9646 

3-4 

14.8 

•4595 

15-5 

31-6 

.9810 

3-5 

15 - 

.4667 

16. 

32.1 

.9969 

3-6 

15.2 

•4737 

16.5 

32.6 

1.0123 

3-7 

15-4 

.4805 

17 - 

33 -i 

1.0272 

3-8 

15.6 

.4872 

17-5 

33-6 

1.0417 

3-9 

15.8 

•4937 

18. 

34 - 

1.0588 

4 - 

16. 

. 5000 

18.5 

34-5 

1.0725 

4.2 

16.4 

.5122 

19. 

35 - 

1.0857 

4.4 

16.8 

•5238 

19-5 

35-4 

1.1017 

4.6 

17.2 

•5343 

20. 

35-9 

1.1142 

4.8 

17.6 

•5454 

20.5 

36.3 

1.1295 

5 . 

17.9 

•5587 

21. 

36.8 

1-1413 

5-2 

18.3 

•5683 

21.5 

37-2 

I-I 559 

5-4 

18.7 

•5775 

22. 

37-6 

1.1702 

5-6 

I 9 * 

•5895 

22.5 

38.1 

1.1S11 

5-8 

19-3 

.6010 

23 - 

38.5 

1.1948 

6. 

19.7 

.6091 

23-5 

38.9 

1.2082 

6.2 

20. 

.6200 

24. 

39-3 

1.2214 

6.4 

20.3 

.6305 

24-5 

39-7 

1 *2343 

6.6 

20.6 

.6408 

25 

40.1 

1.2469 

6.8 

20.9 

•6507 

26 

40.9 

1.2714 

7 - 

21.2 

.6604 

27 

41.7 

1.2950 

7.2 

21.5 

.6698 

28 

42.5 

1.3176 

7-4 

21.8 

.6789 

29 

43-2 

1.3426 

7.6 

22.1 

.6878 

30 

43-9 

1.3667 

7.8 

22.4 

.6964 

3 i 

44-7 

1.3870 

8. 

22.7 

.7048 

32 

45-4 

1.4097 

8.2 

23. 

.7130 

33 

46.1 

1 .4317 

































THEORETICAL VELOCITIES. 


193 


Correspondent Heights, Velocities, and Times of Falling 

Bodies—( Continued .) 


H = — 

v = 


7 f 3 

H = —- 

V — y 2 £-H 

v f 

Head in feet. 

Velocity in feet 

Time 

Head in feet. 

Velocity in feet 

Time 

per second. 

in seconds. 

per second. 

in seconds. 

34 

46.7 

1.4561 

77 

70.4 

2.1874 

35 

47-4 

I.4768 

78 

70.9 

2.2003 

36 

48.1 

I.4968 

79 

71-3 

2.2l6o 

37 

48.8 

I.5164 

80 

71.8 

2.2284 

38 

49-5 

1-5354 

81 

72.2 

2.2438 

39 

50.1 

1-5569 

82 

72.6 

2.2590 

40 

50.7 

1-5779 

83 

73-1 

2.2709 

4 i 

51-3 

1.5984 

84 

73-5 

2.2857 

42 

52 . 

1.6154 

85 

74.O 

2.2973 

43 

52.6 

1.6350 

86 

74-4 

2.3118 

44 

53-2 

1.6541 

87 

74-8 

2.3262 

45 

53-8 

1.6729 

88 

75-3 

2-3373 

46 

54-4 

1.6912 

89 

75-7 

2.3514 

47 

55 - 

1.7090 

90 

76.1 

2.3653 

48 

55-6 

1.7266 

9 i 

76.5 

2.3791 

49 

56.2 

1 •7438 

92 

76.9 

2.3927 

50 

56.7 

1.7637 

93 

77-4 

2.4031 

5 i 

57-3 

1.7801 

94 

77.8 

2.4165 

52 

57-8 

1-7993 

95 

78.2 

2.4297 

53 

58.4 

1.8151 

96 

78.6 

2.4427 

54 

59 - 

1.8305 

97 

79.0 

2-4557 

55 

59-5 

1.8487 

98 

79-4 

2.4685 

56 

60. 

1.8667 

99 

79.8 

2.4812 

57 

60.6 

1.8812 

100 

80.3 

2.4907 

58 

61.1 

1.8985 

125 

89.7 

2.7871 

59 

61.6 

1.9^6 

150 

98.3 

3.0519 

60 

62.1 

1.9324 

175 

106 

3.3019 

61 

62.7 

1.9458 

200 

1 14 

3.5088 

62 

63.2 

1.9620 

225 

120 

3-7500 

63 

63.7 

1.9780 

250 

126 

3-9683 

64 

64.2 

1.9938 

275 

133 

4-1353 

65 

64.7 

2.0093 

300 

139 

4 - 3 I 65 

66 

65.2 

2.0245 

350 

150 

4.6667 

67 

65-7 

2.0396 

400 

160 

5.0000 

68 

66.2 

2.0544 

450 

170 

5.2941 

69 

66.7 

2.0690 

500 

179 

5.5866 

70 

67.1 

2.0864 

550 

188 

5.8511 

7 i 

67.6 

2.1006 

600 

197 

6.0914 

72 

68.1 

2.1145 

700 

212 

6.6038 

73 

68.5 

2.1313 

800 

227 

7.0485 

74 

69. 

2.1449 

900 

241 

7.4689 

75 

76 

69-5 

69.9 

2.1583 

2.1745 

1000 

254 

7.8740 



























CHAPTEK XL 


FLOW OF WATER THROUGH ORIFICES. 

200. Motion of the Individual Particles.—If an 

aperture is made in the bottom or side of a tank, tilled with 
water, the particles of water will move from all portions of 
the body toward the opening, and each particle flowing out 
will arrive at the aperture with a velocity, V, dependent 
upon the pressure or head of water upon it, and, as we shall 
see hereafter, upon its initial position. 

201. Theoretical Volume of Efflux. —If we assume 
the fluid veins to pass out through the orifice parallel with 
each other, and with a velocity due to the head upon each, 
and the section of the jet to be equal to the area, S, of the 
orifice, then the theoretical volume, or quantity, Q , of dis¬ 
charge will equal S x V = & V2gII; A” being the head upon 
the centre of the orifice, and g the acceleration of gravity 
per second = 32.2 feet. We have then for the theoretical 
volume 

Q = S V2gII. 

202. Converging Path of Particles.— The particles 
are observed to approach the orifice, not in parallel veins, 
but by curved converging paths, and if the partition is 
“thin” the convergence is continued slightly beyond the 
partition, a distance dependent upon the velocity of the 
particles. 

203. Classes of Orifices.— If the top of the orifice is 
beneath the surface of the water, the orifice is termed a sub¬ 
merged orifice, and if the surface of the water is below the 




RATIO OF MINIMUM SECTION OF JET. 


195 


top of the orifice, the notch is termed a “weir” We are 
now to consider submerged orifices. 

204. Form of Submerged Orifice-jet— In Fig. 20 
is shown a submerged circular orifice in thin partition. 



In Fig. 21 are delineated more clearly the proportions 
of the issuing jet at the contracted vein, or rend contractd, 
as it was termed by Newton. The form of the contracted 
vein has been the subject of numerous measurements, and 
as the result of late experiments writers now usually assign 
to the three dimensions FK, fit, and LI, the ratios 1.00, 
0.7854, 0.498, as mean proportions of circular jets not ex¬ 
ceeding one-lialf foot diameter. 

205. Ratio of Minimum Section of Jet. —The par¬ 
ticles of the jet that arrive at the centre of the orifice have a 
direction parallel with the axis of the orifice. The particles 
that arrive near the perimeter have converging directions, 
and since they have individually both weight and velocity, 
they have also individual force or momentum in their direc¬ 
tions. This force must be deflected into a new direction, 
and as it can be most easily deflected through a curved 























196 FLOW OF WATER THROUGH ORIFICES. 

path, the curve is continued until the particles have paral¬ 
lelism. The point where the direction of the particles is 
parallel is at a distance from the inside of a small square- 
edged orifice, equal to about one-half the diameter of the 
orifice, and the diameter of the jet at that point is equal 
to about 0.7854 of the diameter of the orifice. The cross- 
section of a circular jet at the same point has therefore a 
mean ratio to the area of the orifice as (0.7854) 2 to (1.00)’, 
or as 0.617 to 1.00. 

206. Volume Of Efflux. —If the velocity due to the 
head upon the center of the orifice is the mean velocity of 
all the particles of the jet, then we have for the volume of 
discharge, 

Q = 0.617 S x V, or Q = 0.617 SV2gH. (2) 

The real volume, Q, of the jet, and its ratios of velocity 
and of contraction, have been the subjects of many obser¬ 
vations, and have engaged the attention of the ablest ex¬ 
perimentalists and hydraulicians, from time to time, during 
many years. 

207. Coefficient of Efflux. — In every jet flowing 
through a thin orifice there is a reduction of the diameter 
of the jet immediately after it passes the orifice. Some 
fractional value of the area S, or the velocity V, or the 
the theoretical volume Q , must therefore be taken—that is, 
they must be multiplied by some fraction coefficient to com¬ 
pensate for the reduction of the theoretical volume of the 
jet. This fractional coefficient is termed the coefficient of 
discharge. Place the symbol c to represent this coefficient, 
and the formula for volume of discharge becomes 

Q — cSV2gH (3) 

208. Maximum Velocity of the Jet. —The point 
where the mean velocity of the particles is greatest is in the 




PRACTICAL USE OF A COEFFICIENT. 


197 


least section of the jet, and here only can it approximate to 
VZgH. The mean velocity will be less at the entrance to 
the orifice, and also after passing the contraction, than in 
the contraction. When speaking of the velocity of the par¬ 
ticles or of the jet hereafter, in connection with orifices, the 
maximum velocity—that is, the velocity in the contraction 
—is referred to, unless otherwise specially stated. 

209. Factors of the Coefficient of Efflux.- If the 
edges of the orifice are square, the circumferential particles 
of the jet receive some reaction from them ; therefore only 
the axial particles can have a velocity equal to V2gH, and 
the mean velocity is a small fraction less. 

In such case the general coefficient of discharge (c) will 
be the product of two factors, one representing the reduc¬ 
tion of velocity, and the other the reduction of the sectional 
area of the jet. 

We shall have occasion to investigate these factors after 
we have determined the value of the general coefficient. 

210. Practical Use of a Coefficient. —The usefulness 
of a coefficient, wdien it is to be applied to new computa¬ 
tions, depends upon its accord with practical results. 

All new and successful hydraulic constructions of orig¬ 
inal design must have their proportions based upon com¬ 
putations previously made. Those computations must be 
founded upon hydrodynamic formulae in which the co¬ 
efficient performs a most important office. In fact the 
skillful application of formulae to hydraulic designs de¬ 
pends upon the skillful adaptation of the one or more co¬ 
efficients therein. 

The coefficient product adopted must harmonize with 
results before obtained, practically or experimentally, and 
the parallelism of all the conditions of the old or experi¬ 
mental structure and the new design cannot be too closely 



198 


FLOW OF WATER THROUGH ORIFICES. 


scrutinized when an experimental result is to control a new 
design for practical execution. 

211. Experimental Coefficients. —A few experimental 
results are here submitted as worthy of careful study. 

From Michelotti. — The following table of experi¬ 
ments with square and circular orifices, by Michelotti, we 
find quoted by Neville.* They refer to a very carefully 
made set of experiments, with an extensive apparatus 
specially prepared, near Turin, where the apparatus was 
supplied with the waters of the Doire by a canal. 

The table is given by Neville in French measures, but 
they are given here as we have reduced them to English 
measures. 

TABLE No. 41. 

Coefficients from Michelottfs Experiments. 


Description, and Size of Orifice, 
in Feet. 


Depth upon 
the center of 
the orifice 
in feet. 


Quantity Time of 

discharged in discharge in 
cubic feet. seconds. 


cubic feet. 


Resulting 
coefficients 
of discharge. 


7.05 561.240 

7.30 685.762 


600 

720 

510 

600 

300 

360 

900 

900 

600 

1800 

1440 

3600 

900 

720 

480 

1800 

1680 

1200 

3600 

3600 

3600 


.619 

.619 

.610 

.6ll 

.612 

.613 

.660 

•645 

•643 

.628 

.612 

.625 

.6ll 

.6lO 

.612 

.6l6 

.605 

.605 

.619 

.620 

.621 

.619 

.619 


Square orifice, 3.197" x 3.197" J 12.43 625.652 

= .071 square foot section.. .. ' 12.59 741.036 



23.13 502.931 

23.14 604.362 


* Hydraulic Tables, by John Neville, C. E. ; M.R.I.A., London, 1853. 

















EXPERIMENTAL COEFFICIENTS. 


199 


From Abbe Bossut. —From experiments made by tlie 
Abbe Bossut we have the following results, as reduced to 
English measures: 


TABLE No. 4 2. 

Coefficients from Bossut’s Experiments. 


Description, Position, and Size of Orifice, 

IN INCHES. 

Depth of the 
centre of 
the orifice, 
in feet. 

Discharge, 
in cubic 
feet per 
minute. 

Resulting 

coefficient. 

Lateral and circular, .53289" diameter. 

9-59 

I.O96 

.613 

“ “ “ 1.06578" “ . 

9-59 

4-344 

.617 

“ “ “ .53289" “ . 

4-273 

•723 

.616 

“ “ “ 1.06578" “ . 

4-273 

1-952 

.619 

“ “ “ 1.06578" “ . 

.0529 

-341 

.649 

Horizontal and circular, .53289" diameter. 

12.54 

1-255 

.614 

“ “ “ 1.06578" “ . 

12.54 

5-040 

.617 

“ “ “ 2.13156" “ . 

12.54 

20.201 

.618 

Horizontal and square, 1.06578" x 1.06578".... 

12.54 

6.417 

.617 

“ “ “ 2.13156" x 2.13156".... 

12.54 

25 - 7 I 7 

.618 

Horizontal and rectangular, 1.06578" x .26644". 

12.54 

T -593 

.613 


From Rennie.— We have also, from experiments of 
Rennie with circular and square orifices, under low heads, 
the following: 


TABLE No. 43. 

Coefficients for Circular Orifices. 


Heads at the centre 
of the orifice, 
in feet. 

\ inch 
diameter. 

\ inch 
diameter. 

i inch 
diameter. 

1 inch 
diameter. 

Mean Values. 

I 

.671 

•634 

.644 

•633 

•645 

2 

.653 

.621 

.652 

.619 

•636 

3 

.660 

.636 

.632 

.628 

•639 

4 

.662 

.626 

.614 

•584 

.621 

Means. 

.661 

.629 

.635 

.616 

•635 








































200 


FLOW OF WATER THROUGH ORIFICES. 


Coefficients for Rectangular Orifices. 


Heads at the 
centre of gravity, 
in feet. 

1 inch x 1 inch. 

2 inches wide 
x £ inch high. 

U inches wide 
x | inch high. 

Equilateral 
triangle of 

1 square inch, 
base down. 

Same triangle, 
with base up. 

I 

.617 

.617 

.663 

- 

.596 

2 

.635 

•635 

.668 

— 

•577 

3 

.606 

.606 

.606 

— 

•572 

4 

•593 

•593 

•593 

•593 

•593 

Means. 

.613 

.613 

.632 

•593 

•585 


f 


From Castel.—In 1836, M. Castel, the accomplished 
hydraulic engineer of the city of Toulouse, made with care 
certain experiments "by request of JD’ Aubuisson, to determine 
the volume of water discharged through apertures in thin 
partitions. 

He placed a dam of thin copper plate in a sluice which 
was 2.428 feet broad, and in the plate opened three rectan¬ 
gular apertures, each 3.94 inches wide and 2.36 inches high. 
The distance between the orifices w r as 3.15 inches. The 
flow took place under constant heads of 4.213 inches above 
the centres of gravity of the orifices, with contractions as 


follows: 

c Coefficient for the middle.6198 

One orifice open, -j “ “ right.6192 

( “ “ left.6194 

{ Coefficient for the two outsides.6205 

“ “ middle and right.6205 

“ “ “ “ left.6207 

Three orifices open, coefficient for all.6230 


Subsequently, he experimented with two orifices, 1.97 
inches wide and 1.18 inches high, with results as follows : 


Head. 


No. 


of orifices open. 


Coefficient. 


3-379 

6.693 



.621 

.622 



.619 

.621 










































EXPERIMENTAL COEFFICIENTS. 


201 


When more than one aperture was open in these exper¬ 
iments of Castel, the volume of water discharged induced 
considerable velocity in each of the supplying sluices. 
This actually increased the effective head. Its effect is here 
recorded in the coefficient instead of in the head, conse¬ 
quently an increased coefficient is given. 

In such cases the real head is the observed head in¬ 
creased by the head due to the velocity of approach = 


H + 


V 2 

64.4* 


From Lespinasse. —From among experiments on a 
larger scale, the following by Lespinasse, with a sluice of 
the canal of Languedoc, are of interest: 


TABLE No. 44. 
Coefficients Obtained by Lespinasse. 


Openings. 

Head on the 
Centre. 

Discharge in 
One Second. 

Coefficient. 

Breadth. 

Height. 

Area. 

Feet. 

Feet. 

Sq. feet. 

Feet. 

Cubic feet. 


4.265 

I.805 

7-745 

14-554 

145.292 

.613 

<< 

I.640 

6.992 

6.631 

92-635 

.641 

a 

I.640 

6.992 

6.247 

88.221 

.629 

a 

I.509 

6.466 

12.878 

138.937 

.641 

a 

1.575 

6.723 

I3-586 

128.764 

.647 

a 

1-575 

6.723 

6-394 

83.948 

.616 

a 

1-575 

6.723 

6.217 

79-857 

•594 

<< 

1-575 

6.717 

6.480 

85.219 

.621 


From Gen. Ellis. —Gen. Theo. G. Ellis has reported 
in a paper* presented to the American Society of Civil 
Engineers, the results of some experiments very carefully 
conducted by him at the Holyoke testing flume in the sum¬ 
mer of 1874. 


* Hydraulic Experiments with Large Apertures. Jour. Am. Soc. Civ. Eng., 
187 G, Vol. V, p. 19 . 






















202 


FLOW OF WATER THROUGH ORIFICES. 


The coefficients for the minimum, mean, and maximum 
velocities are given to indicate generally the range, and the 
results obtained by Gen. Ellis. 

The volume of water discharged was determined by 
weir measurement, and computed by Mr. James B. Fran¬ 
cis’ formula. 

The edges of the orifices were plated with iron about 
one-half inch thick, jointed square. 

Vertical Aperture, 2 ft. x 2 ft. 

Minimum head, 2.061 feet. Coefficient, .60871 I Centre of aperture, 1.90 feet 
Mean “ 3.037 “ “ *59676 > above top of weir. 

Maximum “ 3*538 “ “ .60325 ) Temp, of water, 73 0 Fah. 

Vertical Aperture, 2 ft. horizontal x 1 ft. vertical. 

Minimum head, 1.7962 feet. Coefficient, .59748 I Centre of aperture, 2.40 feet 
Mean “ 5.7000 “ “ *59672 > above top of weir. 

Maximum “ 11.3150 “ “ .60572 ) Temp, of water, 76° Fah. 

Vertical Aperture, 2 feet horizontal x .5 feet vertical. 

Minimum head, 1.4220 feet. Coefficient, .61165 ) Centre of aperture, 2.15 feet 
Mean “ 8.5395 “ “ .60686 >• above top of weir. 

Maximum “ 16.9657 “ “ .60003 ) Temp, of water, 76" Fah. 

Vertical Aperture, i ft. x 1 ft. 

Minimum head, 1.4796 feet. Coefficient, .58230 
Mean “ 9.8038 “ “ .59612 

Maximum “ 17.5647 “ “ *59687 

Horizontal Aperture, i ft. x i ft. and Slightly Submerged 

Issue. 

Minimum head, 2.3234 feet. Coefficient, .59871 ) 

Mean “ 8.0926 « “ .60601 f- Top Surface of orifice 441 

Maximum “ 18.4746 “ “ .60517) feet above crest of weir. 

Horizontal Aperture (in plank) with Curved Entrance and 

Slightly Submerged Issue. 

Minimum head, 3.0416 feet. Coefficient, .95118) 

Mean “ 10.5398 “ “ .94246 V IsSUe about level with crest 

Maximum “ 18.2180 “ “ .94364 ) of weir ‘ 


COEFFICIENTS DIAGRAMMED. 


203 


Tlie range, and results generally, of Gen. Ellis’ experi¬ 
ments with circular vertical orifices, are indicated by the 
following extracts from his extended tables: 


TABLE No. 45. 

Coefficients for Circular Orifices, obtained by Gen. Ellis. 


Diameters. 

Head. 

Coefficients. 

2 feet. 

1.7677 feet. 

.58829 

(( u 

5.8269 “ 

.60915 

u u 

9-638 1 “ 

•6153° 

I foot. 

1.1470 feet. 

•57373 

u a 

10.8819 “ 

•59431 

u u 

17.7400 “ 

•59994 

.5 foot. 

2.1516 feet. 

.60025 

a u 

9.0600 “ 

.60191 

u u 

17.2650 “ 

.59626 


212. Coefficients Diagrammed.— The coefficients, as 
developed by the several experimenters, seem at first glance 
to be very fitful, and without doubt the apparatus used 
varied in character as much as the results obtained 

To arrange all the series of coefficients that appeared to 
have been obtained by a reliable method, in a systematic 
manner, we have plotted all to a scale, taking the heads 
for abscisses and the coefficients for ordinates. The curves 
thus developed were brought into their proper relations, 
side by side, or interlacing each other. 

Then we were able to plot in the midst of those curves 
the general curves due to each class of orifice under the 
several heads, and those apparently due to the law govern¬ 
ing the flow of water through submerged orifices. 

From these curves we have prepared tables of coefficients 
for various rectangular orifices, with greatest dimension, 











204 


FLOW OF WATER THROUGH ORIFICES. 


both horizontal and vertical, with ratios of sides varying 
from 0.125 to 1, to 4 to 1, and for heads varying from 
0.2 feet to 50 feet. 

All of the curves increase from that for very low heads 
rapidly as the head increases, until a maxima is readied, 
and then decrease gradually until a minima is readied, 
and then again increase very gradually, the head in¬ 
creasing all the time. This increase, and decrease, and 
increase again of the coefficients, arranges them, when thus 
plotted, into two curves of opposite flexure, and with all 
the curves tending to pass through one intermediate point. 

213. Effect of Varying the Head, or the Propor¬ 
tions of the Orifice. —The effect of increasing or decreas¬ 
ing the head upon a given orifice is clearly shown by the 
several columns of coefficients in Tables 46 and 47. 

The effect of increasing or decreasing the ratio of the 
base to the altitude of an orifice will be manifest by tracing 
the lines of coefficients horizontally through the two tables, 
for any given head. 

These effects should be duly considered when a coef¬ 
ficient is to be selected from the table for a special appli¬ 
cation. 

The coefficients apply strictly to orifices with sharp, 
square edges, and with full contraction upon all sides. The 
heads refer to the full head of the water surface, and not to 
the depressed surface over or just in front of an orifice when 
the head is small. 

A very slight rounding of the edge would increase the 
coefficient materially, as would the suppression of the con¬ 
traction upon a portion of its border by interference with 
the curve of approach of the particles. 


COEFFICIENTS DIAGRAMMED. 


205 


TABLE No. 46. 

Coefficients for Rectangular Orifices. 

In thin vertical partition, with greatest dimension vertical. 


Breadth and Height of Orifice. 


Head upon 
centre of orifice. 

4 feet high, 

1 foot wide. 

2 feet high, 

1 foot wide. 

i£ feet high, 

1 foot wide. 

1 foot high, 

1 foot wide. 

Feet. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

.6 


• • • • 

• • • 

•5984 

•7 


• • • • 

■ • • • 

•5994 

.8 


• • • • 

.6130 

.6000 

•9 


• • • • 

.6134 

.6006 

i 

• • • • 

• • • • 

•6135 

.6010 

1.25 


.6188 

.6140 

.6018 

1.50 


.6187 

.6144 

.6026 

i*75 


.6186 

.6145 

•6033 

2 


.6183 

.6144 

.6036 

2.25 


.6180 

.6143 

.6039 

2 -5 

.6290 

.6176 

.6139 

.6043 

2*75 

.6280 

.6173 

.6136 

.6046 

3 

.6273 

.6170 

.6132 

.6048 

3*5 

.6250 

.6160 

.6123 

.6050 

4 

.6245 

.6150 

.6lIO 

.6047 

4-5 

.6226 

.6138 

.6lOO 

.6044 

5 

.6208 

.6124 

.6088 

.6038 

6 

.6158 

.6094 

.6063 

.6020 

7 

.6124 

.6064 

.6038 

.6011 

8 

.6090 

.6036 

.6022 

.6010 

9 

.6060 

.6020 

.6014 

.6010 

10 

• 6o 35 

.6015 

.6010 

.6010 

15 

.604O 

.6018 

.6010 

.6011 

20 

.6045 

.6024 

.6012 

.6012 

25 

.6048 

.6028 

.6014 

.6012 

3° 

.6054 

.6034 

.6017 

.6013 

35 

.6060 

.6039 

.6021 

.6014 

40 

.6066 

.6045 

.6025 

.6015 

45 

.6054 

.6052 

.6029 

.6016 

5° 

.6086 

.6060 

.6034 

.6018 




















206 


FLOW OF WATER THROUGH ORIFICES. 


TABLE No. 4 7. 

Coefficients for Rectangular Orifices. 

In thin vertical partition, with greatest dimension horizontal. 


Breadth and Height of Orifice. 


Head upon 
centre of orifice. 


Feet. 

0.2 

•3 

•4 

*5 

.6 

•7 

.8 

•9 

1 

1.25 

T * 5 ° 

1 - 75 

2 

2.25 
2.5° 

2 - 75 

3 

3 - 5 ° 

4 

4- 50 

5 

6 

7 

8 

9 

10 

T 5 

20 

2 5 

30 

35 

40 

45 

5 ° 


0.75 feet high, 
1 foot wide. 


Coefficient. 


.6050 

.6063 

.6074 

.6082 

.6086 

.6090 

.6095 

.6lOO 

.6103 

.6104* 

.6103 

.6102 

.6lOI 

.6lOO 

.6094 

.6085 

.6074 

.6063 

.6044 

.6032 

.6022 

.6015 

.6010 

.6012 

.6014 

.6016 

.6018 

.6022 

.6026 

.6030 

• 6o 35 


0.50 feet high, 
1 foot wide. 


Coefficient. 


.6140 

.6150 

.6156 

.6162 

.6165 

.6168 

.6172 

. 6173 * 

.6172 

.6168 

.6166 

.6163 

•6157 

•6155 

•6153 

.6146 
.6136 
.6125 
.6114 
.6087 
.6058 
•6033 
.6020 
• .6010 
.6013 
.6018 
.6022 
.6027 
.6032 
.6037 
.6043 
.6050 


0.25 feet high, 
1 foot wide. 


Coefficient. 

.6293 

.6306 

•6313 

•63 T 7 

.63 1 9 

.6322 

.6323* 

.6320 

.6317 

• 6 3 1 3 

.6307 

.6302 

.6293 

.6282 

.6274 

.6267 

.6254 

.6236 

.6222 

.6202 

.6154 

.6110 

.6073 

.6045 

.6030 

•6033 

.6036 

.6040 

.6044 

.6049 

•6055 

.6062 

.6070 


0.125 feet high, 
1 foot wide. 


Coefficient. 

•6333 
•6334 
•6334* 
• 6 333 
•633 2 
• .6328 
.6326 
.6324 
.6320 
.6312 
•6303 
.6296 
.6291 
.6286 
.6278 
.6273 
.6267 
.6254 
.6236 
.62 2 2 
.6202 
.6154 
,6114 
.6087 
.6070 
.6060 
.6066 
.6074 
.6083 
.6092 
.6103 
.6114 
.6125 
.6140 

















PECULIARITIES OF EFFLUX. 


207 


214. Peculiarities of Efflux from an Orifice.— 

In Fig. 22, containing a horizontal orifice, the horizontal 
line cutting a has an altitude above the orifice equal to 3.5 
diameters, and the horizontal line cutting e equal to 10 
diameters of the orifice. As the altitude of the water sur- 


Fig. 22 . 



face above a square orifice increases from very low heads to 
the level a , the particles continually find new advantage or 
less hindrance in their tendency to flow out of the orifice, 
possibly by decrease, of the vortex effect accompanying 
very low heads over orifices nearly square ; afterwards the 
resistance increases up to the altitude e, possibly by more 
effective reaction from the inner edges of the orifice, is, 
until gravity is enabled to gather the jet well into a body 
and establish firmly its path. For altitudes greater than 
ten diameters the coefficients for square orifices remain 
nearly constant. 















208 


FLOW OF WATER THROUGH ORIFICES. 


Similar effects are observed when the orifices are rectan¬ 
gles, other than squares, though their first change occurs at 
different depths. 

These phenomena are not fully accounted for by ex¬ 
periment. 

215. Mean Velocity of the Issuing Particles.— 

We have heretofore assumed in our theoretic equations, 
that all the particles of water bcdef g, Fig. 22, will arrive 
at the point of greatest contraction of the issuing jet, with a 
velocity equal to that which a solid body would have ac¬ 
quired by falling freely from e to o, which, according to the 
the theorem of Toricelli, and its demonstrations frequently 
repeated by other eminent philosophers, would be equal to 
V2yIL H beiug equal to the height e o. 

The experiments of Mariotte, Bossut, Miclielotti, Ponce- 
let, Pousseile, and others, covering a large range of areas of 
orifice, and of head, show that this is very nearly correct; 
and the velocity of issue of the axial particles has in some 
of the experiments appeared to slightly exceed the value of 
V2gH. An average of experiments gives the mean velocity 
of the particles as a whole through the minimum section as 
.974 V2gH. 

Their dynamic effect if applied to work should have 
.974 V2gH instead of V2<jH as the factor of velocity. 

216. Coefficients of Velocity and Contraction.— 
We have then, .974 for mean coefficient of velocity , indi¬ 
cating a loss of .026 per cent, of theoretic volume or dis¬ 
charge by reduction of velocity ; .637 for mean coefficient 
of contraction , indicating a loss of 36.3 per cent, of theoretic 
volume by contraction ; and .62 nearly for mean coefficient of 
discharge , including all losses, a total of about 38 per cent. 

The coefficient of velocity we will designate by c v , and 
the coefficient of contraction by c c . 






VOLUME OF EFFLUX FROM A SUBMERGED ORIFICE. 209 


Then c v x c c = c = coefficient of discharge or volume. 

217. Velocity of Particles Dependent upon tlieir 
Angular Position. —Bayer assumed the hypothesis that, 
the velocities of the particles approaching the orifice from 
all sides are inversely as the squares of their distances from 
its centre, hut this should undoubtedly be applied only to 
particles in some given angular position. 

Gravity will not act with equal force in the direction of 

the orifice, upon each of the particles e,f, g , and 7^, Fig. 22, 

though they are all equally distant from 0 , but more nearly 

in the ratios of the cosines of the angles eoe , eof , eog , etc., 

and it is not probable that the particle h will acquire a 

velocity at its maximum through the contraction, quite 

equal to that which e will acquire. If the velocity of e is 

assumed equal to unity, and the mean velocity of all the 

particles equal to .974, then, according to the hypothesis of 

the angular distance, the mean velocity will be that due to 

particles having their cosines equal to .974, or an angular 

* 

distance of 13°, as at b and/. 

218. Equation of Volume of Efflux from a Sub¬ 
merged Orifice. —Neville suggests a formula* for the 
discharge of water from rectangular orifices, more theoreti¬ 
cally exact than the above simple formulas, as follows : 


D = c 'V'Zgh x | A 


\7i + id) t — Qi — \d) f 

dlA 


( 4 ) 


when B = volume of discharge, 

A = area of orifice, 

h = head upon the centre of the orifice, 
d = depth of the orifice, or distance between its 
bottom and top, 
c = coefficient of discharge. 


* Third Edition of Hydraulic Tables, page 48 . London, 1875 . Also vide 
equation 3 , page 283 , ante. 






210 


FLOW OF WATER THROUGH ORIFICES. 


This formula can be advantageously applied when the 
orifice is large and but slightly submerged, as is frequently 
the case with sluice gates controlling the flow of water from 
storage reservoirs or canals into flumes leading to water¬ 
wheels, or with head-gates of races or canals. 

Good judgment must, however, be exercised in each case 
in the selection of the coefficient of velocity (c v ) and the co¬ 
efficient of contraction (c c ), the factors of c, especially the 
coefficient of contraction (§ 21G), which is usually much the 
most influential of the two. (Vide §370, p. 360.) 

219. Effect of Outline of Symmetrical Orifices 
upon Efflux. —According to the various series of experi¬ 
ments, the coefficient for a circular orifice under any given 
head is substantially the same as for a square orifice under 
the same head, and it is probable that the coefficients for 
elliptical orifices is substantially the same as that for their 
circumscribing rectangles. 

220. Variable Value of Coefficients. —The coeffi¬ 
cients obtained by careful experiment and recorded above, 
as also tables of coefficients, indicate unmistakably that the 
value of c in the equation 

Q = cS V2gH 

is a variable quantity, and that a general mean coefficient 
cannot be used universally when close approximate results 
are desired, but that, for a particular case, reference should 
always be made to a coefficient obtained under conditions 
similar to that of the case in question. 

221. Assumed Mean Volume of Efflux. —In ordi¬ 
nary approximate calculations, and in general discussions 
of formulas for square and circular orifices, whether the jet 
issues horizontally or vertically, it is customary to assume 
0.62 as the ratio of the actual to the theoretical volume of 



CIRCULAR, AND OTHER FORMS OF JETS. 


211 


discharge. This makes the equation for ordinary calcu¬ 
lations : 

Q = .62 8V2gS, or Q = .62 SV. (5) 

The expression for effect of acceleration of gravity (2 g) 
being a constant quantity, may be combined with the co¬ 
efficient, when (.62 V2g = 4.9725) we have the equation 

Q — 4.9725$ V11, or approximately, Q = 5.$ V H. (6) 

Q being the discharge in cubic feet in one second, it will be 
multiplied by 60 to determine the discharge in one minute, 
and by 3600 to determine the discharge in one hour. 

222 . Circular, and other Forms of Jets. —A cir¬ 
cular aperture, with full contraction, gives a jet always 
circular in section, until it is broken up into globules by 
the effects of the varying velocities of its molecules and the 
resistance of the air. Through the vend contractd its form 
is that of a truncated conoid. 

Polygonal and rectangular orifices give jets that continu¬ 
ally change their sectional forms as they advance. 

Fig. 22 a, from D’Aubuisson’s Treatise on Hydraulics, 
illustrates the transformations of 
forms of a jet from a square orifice, 

AC EG. The jet is square at the 
entrance to the aperture, assumes 
the form bcdefgha a short distance 
in front of it, and the form ctc'e'g' a 
short distance further on, and con¬ 
tinues to assume new forms until 
its solidity is destroyed. Symmetrical orifices, without re¬ 
entrant angles, give symmetrical jets that assume symmet¬ 
rical, varying sections. 

Star-shaped and irregular orifices, upon close observa- 


Fig. 22 a. 






212 


FLOW OF WATER THROUGH ORIFICES. 


tion, are found to give very complex forms of jets. Their 
coefficients of efflux have not been fully developed by ex¬ 
periment. 

223. Cylindrical and Divergent Orifices.—In Fig. 

23 and Fig. 24 showing cylindrical and divergent orifices, 
if the diameters, is, of the orifices, are greater than the 


Fig. 23 . Fig. 24 . Fig. 25 . Fig. 26 . 



thickness of the partitions, the coefficients of discharge will 
remain the same as in thin plate. In such cases the jets 
will pass through the orifices without touching them, ex¬ 
cept at the edges, is. Such orifices are also termed thin. 

224. Converging Orifices. —In Fig. 25 and Fig. 26, 
showing converging orifices in thin partitions, if the diam¬ 
eters, is, are taken, the coefficients will be reduced to .58, or 
a little less; but if the diameters, ot , are taken, the co¬ 
efficients will be increased nearly to .90, and will be greater, 
for any given velocity, in proportion as the forms of the 
orifices approach to the form of the perfect vend contractd, 
for that velocity. 

When the converging sides of the orifice in Fig. 25, pro¬ 
longed, include an angle of 16°, the coefficient should be 
about .93, and when in Fig. 26 the sides of the orifice are in 
the form of the vend contractd, the coefficient should be 
about .95. 






























PUMPING STATION, MANCHESTER. 





























































































































































































































































































CHAPTEB XII. 


FLOW OF WATER THROUGH SHORT TUBES. 

225 . An Ajutage. —If a cylindrical orifice is in a parti¬ 
tion whose thickness is equal to two-and-one-half or three 
times the diameter of the orifice ; or if the orifice is a tube 
of length equal to from two and one-half to three interior 
diameters, then the orifice is termed a short tube , or ajutage. 
The sides of short tubes may be parallel, divergent , or con¬ 
vergent . 

226 . Increase of Coefficient. —There is an influence 
affecting the flow of water through short cylindrical tubes, 
Fig. 28, sufficient to increase the coefficient materially, that 
does not appear wdien the flow is through thin partition. 
The contraction of the jet still occurs as in the flow through 
thin partition, but after the direction of the particles has 
become parallel in the vend contractd , a force acting from 
the axis of the jet outward, together with the reaction from 
the exterior air, begins to dilate the section of the jet and 
to fill the tube again. The tube is in consequence again 
filled at a distance, depending upon the ratio of the velocity 
to the diameter, of about two and one-half diameters from 
the inner edge of the orifice. The axial particles of the jet, 
not receiving so great a proportion of the reaction from the 
edges of the orifice as the exterior particles, obtain a greater 
velocity. A portion of their force is transmitted to their 
surrounding films through divergent lines, and the velocity 
of the exterior particles within the tube is augmented, and 
the section of the jet is also augmented, until its circumfer- 


214 


FLOW OF WATER THROUGH SHORT TUBES. 


ence touches the tube. At the same time, the transmission 
of force from the axis toward the circumference tends to 
equalize the velocity of the particles throughout the section, 
and to materially reduce their mean velocity, and conse¬ 
quently the coefficient of velocity, c v . 

227. Ajutage Vacuum and its Effect. — Immedi¬ 
ately upon the issue of the jet, beyond the contraction, the 
velocity of the particles tends to impel forward the impris¬ 
oned air, and as soon as the tube tills to cause a vacuum* 
about the contraction. The full force of gravity is here act¬ 
ing upon the jet in the form of velocity ; the jet is therefore 
without pressure in a transverse direction. 

As soon as the exterior of the jet is relieved from the 
pressure of the atmosphere about the contraction, its par- 
tides are deflected to parallelism with less force and in a 
shorter distance from the entrance to the aperture, and the 
contraction is consequently lessened; also the pressure of 
the atmosphere upon the reservoir surface tends to augment 
the velocity of entry of the particles into the aperture 
toward the vacuum, and atmospheric pressure equally 
resists the issue of the jet, the combined effect resulting in 
the expansion of the jet. 

228. Increased Volume of Efflux. — If the cylin¬ 
drical tube terminates at the point where the moving par¬ 
ticles reach the circumference and fill the tube, and 
before the reaction from the roughness of the interior of 
the tube has begun sensibly to counteract the accelerating 
force of gravity, the capacity of discharge is then found to 
be increased about twenty-five per cent., and the mean co¬ 
efficient becomes .815 approximately, or if the tube projects 


* If the inside of a smooth divergent tube is greased, so as to repel the par¬ 
ticles of water and prevent contact, the vacuum cannot take place. 



DIVERGENT TUBE. 


215 


into the reservoir, .72, instead of .62, as in the orifice in thin 
plate. We have now for the volume of water discharged, 
in cubic feet per second, 

Q = .815 8 V%gH, oyQ = .815 or Q = 6.54 8 VH (1) 

If the section of tjie tube is expressed in terms of the 
diameter, in feet or fractional parts of feet, then since 8 = 
.7854<$ 2 , the equation will become 

Q = 6.54 (.7854d 2 ) VH = 5.137d 2 VH. (2) 

229. Imperfect Vacuum.— If the tube is of less 
length than above indicated, so that the vacuum is not 
perfect, the conditions of flow and the coefficient will be 
similar to that through thin plate; and if the tube is length¬ 
ened, the flow will be reduced by reaction from the interior 
of the tube, in which case the tube will be termed a pipe. 


Fig. 28. Fig. 29. Fig. 80. 



230. Divergent Tube.— When a short divergent tube , 
Fig. 29, is attached by its smaller base to the inside of a 
plane partition, the phenomena of discharge will be similar 
to that through an orifice in thin plate, unless a vacuum 
shall be established about its contraction, as in the case of 















































216 


FLOW OF WATER THROUGH SHORT TUBES. 


short cylindrical tubes. This can only occur when the 
divergence is slight, or the velocity great. 

For ordinary cases, the mean coefficient of discharge 
through square-edged divergent tubes may be taken as . 62, 
but it is subject to considerable variation in tubes of small 
divergence, as the divergences, the ratio of length to diam¬ 
eter, and the velocity of flow or head varies. 

When a vacuum takes place in a divergent tube, the 
discharge exceeds that from a cylindrical tube with diam¬ 
eter equal to the smaller diameter of the divergent tube, 
and the coefficient of volume may then even become greater 

than unity. 

« 

231. Convergent Tube. —When a short , convergent 
tube , Fig. 30, is attached by its larger base to the inside of 
a plane partition, and its coefficient of flow with a perfect 
vacuum is determined for its diameter of entrance, as above 
in the cases of thin plate, cylindrical and divergent tubes, 
then the coefficient of volume will be found to decrease as 
the angle of convergence increases. 

Contraction will take place as in thin plate, until the 
angle of convergence, that is, the included angle between 
the sides produced, exceeds 13°, and a vacuum will also be 
produced ; but the exterior of the jet will reach the inner 
circumference and fill the tube at a shorter distance from 
the point of least contraction, as the angle increases, and 
the augmenting effect of the vacuum will be reduced. 

232. Additional Contraction. —There is always an 
additional contraction just after the exit of the jet from 
convergent tubes. 

The coefficient of discharge will remain in excess of the 
coefficient for thin plate until the second contraction equals 
that in thin plate, after which the coefficient will be less 
than for thin plate. 


COEFFICIENT OF SMALLER DIAMETER. 


217 


233. Coefficients of Convergent Tubes.—In the 

following table are given the coefficients of discharge for 
the larger and the smaller diameters, also of the velocity , 
for several angles of convergence. The table is based upon 
careful experiments by Castel. The length of the tube was 
2.6 diameters, and the smaller diameter and length of tube 
remained constant. 


TABLE No. 48. 

Castel’s Experiments with Convergent Tubes. 


Smallest diameter = .05085 feet. 


Angle of convergence. 

Larger diameter. 

Smaller diameter. 

Velocity. 

o° o' 

Coefficient. 

O.829 

Coefficient. 

O.829 

Coefficient. 

0.830 

1° 36 ' 

.809 

.866 

.866 

3° 10 

.786 

• 8 95 

• 8 94 

4 0 io' 

.771 

.912 

.910 

5° 26' 

•747 

.924 

.920 

7 ° 5 2 

.691 

•929 

• 93 1 

8° 58' 

.671 

•934 

.942 

IO° 20 

.647 

•938 

• 95 ° 

12° 4 

13 ° 2 4 ' 

.611 

.942 

•955 

•597 

.946 

.962 

14 0 28' 

•577 

.941 

.966 

16 0 36' 

•545 

• 93 8 

.971 

19 0 28' 

• 5 01 

.924 

.970 

21 ° O' 

.480 

.918 

.971 

23 ° O' 

•457 

• 913 

•974 

29 0 58' 

• 39 ° 

.896 

•975 

O / 

40 20 

• 3*9 

.869 

.980 

4 8° 50' 

.276 

• 8 47 

• 9 8 4 


The coefficients for the larger diameter have been com¬ 
puted from the remaining data of the table for insertion 
here. 

234. Increase and Decrease of Coefficient of 
Smaller Diameter.—When the coefficient of volume is 

















218 


FLOW OF WATER THROUGH SHORT TUBES. 


determined for tlie smaller diameter, or issue of a short, 
convergent tube, the coefficient is found to increase from 
that for cylindrical tubes at angle 0° to an angle of about 
13° 30', when, under the conditions upon which Castel’s 
table was based, it has increased from .83 to .95. After¬ 
wards, the coefficient gradually reduces, until at 180° it 
becomes .62, as in thin plate. 

235. Coefficient of Final Velocity.—The coefficient 
of final velocity of issue gradually increases as the angle of 
convergence increases, until it rises from .83 * at angle 0° to 
nearly unity at angle 180°; but that, for angles less than 


13°, is not the true coefficient of 
velocity, since it refers to the ve¬ 
locity of issue at the end of the 
tube, instead of in the contrac¬ 
tion. 


Fig. 31 . 



236. Inward Projecting 
Ajutage.—When an orifice, or 
the entrance of a short tube, is 
projected into the interior of a 
reservoir, as in Fig. 31, the angle 
of approach of the particles be¬ 


comes greater than when the orifice is in plane partition, 
and the contraction becomes still more marked. Borda, 
when experimenting with such a tube, in which the vacuum 
was not perfected, found the coefficient to be .515. This 
coefficient may be considered as an extreme minimum. 

237. Compound Tube.—When two or more of the 
short tubes above described are joined together endwise 
into one tube, as in Fig. 32, the new tube thus formed is 
termed a compound tube. 

* Its mean velocity, in a cylindrical tube, after the jet lias expanded beyond 
the contraction. 

























COEFFICIENTS OF COMPOUND TUBES. 


21 ? 


Fig. 32. 



Venturi experimented witli various forms and propor¬ 
tions of compound tubes, and observed remarkable results 
produced by certain of them, which apparently augmented 
the force of gravity. 

With a tube similar to Fig. 82, but with less perfect 
contraction, having the included angle of the divergent tube 
equal to 5° 6', the smallest diameter equal to 0.1109 feet, 
and the length equal to nine diameters, the coefficient, com¬ 
puted for the smallest diameter, when flowing under a con¬ 
stant head of 2.89 feet, was 1.46, or about 2.4 times that of 
an equal orifice in thin plate. 

238. Coefficients of Compound Tubes.—Other forms 
of compound tubes, with conical diverging ajutages of dif¬ 
ferent lengths and angles, gave results as follows: 


TABLE No. 49. 
Experiments with Divergent Ajutages. 


Ajutage. 

Coefficient. 

Ajutage. 

Coefficient. 

Angie. 

Length. 


Angle. 

Length. 

3° 30' 

Feet. 

O.364 

0.93 

5 ° 44 ' 

Feet. 

.193 

.82 

4 ° 33 ' 

I.095 

1.21 

io° 16' 

.865 

.91 

4 ° 38 ' 

I.508 

1.21 

io° 16' 
14 0 14' 

.147 

.91 

4 ° 38 ' 

I.508 

1-34 

.147 

.61 

5 ° 44 ' 

0-577 

1.02 






































220 


FLOW OF WATER THROUGH SHORT TUBES. 


239. Experiments with Cylindrical and Com¬ 
pound Tubes.— The following table gives interesting re¬ 
sults of experiments by Eytelwein with both cylindrical 
and compound tubes. 

He first experimented with a series of cylindrical tubes 
of different lengths, but of equal diameters ; he then placed 
between the cylindrical tubes and the reservoir a conical 
converging tube of the form of the vend contracta, and 
repeated the experiments; and afterwards added also to 
the discharge end a conical diverging tube with 5° 6' angle, 
Fig. 33. 

Fig. 33. 



TAB LE No. 50. 
Experiments with Compound Tubes. 


Length of tube P in 
diameters. 

Length of tube P 
in feet. 

Coefficient for 
tube P. 

Coefficient for 
tube CP. 

Coefficient for 
tube CPD. 

O.038 

O.OO33 

O.62 

• • • 

• • • • 

I.OOO 

•0853 

.62 

.967 

• • • • 

3.000 

•2559 

.82 

•943 

1.107 

I2.077 

I.0302 

•77 

.870 

.978 

24.156 

2.0605 

•73 

.803 

• 9°5 

3^-233 

3.0907 

.68 

.741 

.836 

48.272 

4.II76 

•63 

.687 

.762 

60.116 

5- T 479 

.60 

.648 

.702 


The diameter of the tube P was 0.0853 feet, and the flow 
took place under a computed average head of 2.3642 feet. 
The mean head was computed by the formula, 





















PERCUSSIVE FORCE OF PARTICLES. 


221 


IF = 


H-h 


.2 {VH - Vh)_ 


( 3 ) 


in which H = maximum head, = minimum head, H' = 
mean head. 

240. Tendency to Vacuum_The effect of the per¬ 

cussion of the axial particles, tending to produce a vacuum, 
and of the enlargement of the circumference of the jet in 1), 
is apparent until the length reaches thirty-six diameters, 
and is greatest at three diameters length, though still less 
than with Fig. 28, because the surface of contact of the jet 
against the tube is greater. 

241. Percussive Force of Particles.—The percus¬ 
sive effect of particles of water in rapid motion is illustrated 
by another experiment of Ventu¬ 
ri's, with apparatus similar to 
Fig. 34. 

A is a high tank kept filled 
with water, and C is a smaller 
tank at its base, full of water at 
the beginning of the experiment. 

P is an open-topped pipe placed 
in the small tank, and has holes 
pierced around its base, so that 
the water in C may enter it freely 
and rise to the level c. From A a small tube, e , leads a jet 
into P. 

Upon the tube e being opened, the whole body of water 
in P is set in motion and begins to flow over its top, and the 
body of water in C is drawn into the pipe P through the 
perforations, and the surface of C will be seen to fall grad¬ 
ually from c to d, until air can enter through the perfora¬ 
tions and destroy the partial vacuum in P. 





















222 


FLOW OF WATER THROUGH SHORT TUBES. 


For a clear conception of the effect of the particles of the 
jet upon the particles in P, imagine all the particles and 
the apparatus to he greatly magnified, so that there will 
appear to he a jet, e, of halls, like billiard halls, for illus¬ 
tration, through a mass, P, of similar halls. 

242. Range of a Set of Eytelwein’s Experiments. 
—In the last table (No. 50), there appears the mean coef¬ 
ficients due to several distinct classes of apertures, viz. : 
0.62 due to a tube orifice or orifice in thin plate, with length 
equal to 0.038 diameters; 0.82 due to a short cylindrical 
tube , with length equal to 3 diameters ; 0.943 due to lessened 
contraction by the convergent entrance, with length equal 
to 3 diameters ; and 1.107 (which in more perfect form of 
compound tube we have found to he 1.46) due to convergent 
entrance and divergent exit, with length equal 3 diameters. 

There also appears the increase of coefficient from orifice 
to short tube , and then the gradual reduction of all the 
coefficients by increase of length of tube (into pipe) from 3 
to 60 diameters long. 

These phenomena cannot fail to he of interest to students 
in that branch of natural philosophy which relates to hydro¬ 
dynamics, and the practical liydraulician cannot afford to 
overlook their effects. 

243. Cylindrical Tubes to be Preferred.—There is 
rarely occasion for the practical and honest use of the 
divergent tube, when its object cannot better be accom¬ 
plished by a slightly increased diameter of cylindrical tube. 
The capability of the divergent ajutage to increase the dis¬ 
charge from a given diameter of orifice, was known to the 
ancient philosophers, and to some of the Roman citizens who 
had grants of water from the public conduits, and W Au- 
buisson states that a Roman law prohibited their use within. 
52J feet of the entrance of the tube. 








illllilllllliilillllllil 




illililll 


liiiiiliiiliiiiiiiliiili l 

i 


iiiiiiiiiiiiiiiiii 






llllllllllllllllllllllllll 




lilllilllllllilliilllilil 

ill i i il l ill i i 1 ill 


Cd 

£ 

»-H 

o 


o 

£ 

t-H 

cu 

a 

D 


eu 

D 

Q 

Q 

£ 

D 

O 

a. 

a 

o 

o 

a; 

o 

H 

O 

55 

HH 

I 

H 

* 

0 



































































































































































































































CHAPTER XIII. 


I 


FLOW OF WATER THROUGH PIPES, UNDER PRESSURE. 

244. Pipe and Conduit.—A cylindrical tube intended 
to convey water under pressure is termed a pipe when its 
length exceeds about three times its interior diameter ; or 
immediately after its length has become sufficient for the 
completion of the vacuum about the jet flowing into it. 

A long pipe constructed of masonry is termed a conduit , 
and when it is a continuous tube, or composed of sections 
of tubes with their axes joined in one continuous line and 
adapted to convey water under pressure, it is termed a main 
pipe , sub-main , branch , waste , or service pipe , according 
to its office. 

245. Short Pipes give Greatest Discharge.—The 

greatest possible discharge through a cylindrical tube, due 
to a given head, occurs when its length is just sufficient to 
allow of the completion of the vacuum about the contrac¬ 
tion of its jet at the influence, if its influent end is then 
sufficiently submerged to maintain the pipe full at the 
issue. 

In the discussion of short tubes (§ 228), we have seen 
that their coefficient of discharge is increased from 0.62 
(that for thin plate) to a mean of 0.815. There is still a loss 
of eighteen per cent, of the theoretical volume, due chiefly 
to the contraction of the vein at its entrance to the tube, 
from which results a loss of velocity and a loss of energy as 
the jet expands to All the tube. 


224 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE. 


LOSS OF FORCE, OR EQUIVALENT HEAD, AT 
THE ENTRANCE TO A PIPE. 


246. Theoretical Volume from Pipes.—Let A, Fig. 

35, be a reservoir containing water one hundred feet deep = 
H, to the level of its horizontal effluent pipe, P. Let the 
pipe P be one foot in diameter — d. 

Then the theoretical volume of discharge will equal 
V2gH x .7854c7 2 = 63.028 cubic feet per second ; but when 
the pipe is three diameters long (= 3 feet), the real discharge 
according to experiment will be 

Q = .815 V2gSx .7854<7 2 , (1) 

* 

= 51.40 cubic feet per second. 


Fig. 35. 



Let V represent the theoretical velocity; then will the 

total head H = =100 feet. 

2g 

Let v represent the measured velocity of discharge, and 


li the head necessary to generate v, then h 





























MECHANICAL EFFECT OF THE EFFLUX. 


225 


24 : 7 . Mean Efflux from Pipes. —The section of the jet, 
having expanded, beyond the contraction issues with a diam¬ 
eter equal to that of the tube, and the coefficient of velocity, 
c,, is consequently equal to the coefficient of discharge, c, 
which is, at a mean, .815 and the theoretical velocity V= 
v v 

— = -gjg = 80.25 feet per second. 


t 


248. Subdivision of the Head. —The total head 1L 
acting upon a short cylindrical tube, consists of two por¬ 
tions, one of which, = 66^ per cent, of U, generates v = 
.815 V = 65.4 feet per second. The remaining 33} per cent, 
of H acts in the form of pressure to overcome the resistance 
of entry of the jet into the tube. Let Ji' be the equivalent 
of the neutralized velocity. 

v 2 

Tlie head due to v is n = 66.5 feet in the above as- 

2 g' 

sumed case, and the head due to — the head due to v is 


1 


\ v 2 

>*9 


7 ; _ / ___ \ (} 

1 \815 2 x2 g 2 gf W 

The ratio of to h is therefore ^ 

case, and (Ji + h’) = (h + .5055 h) = H. 


33.5 feet. 

- l) = .5055 for this 


249. Mechanical Effect of the Efflux. —Since the 
dynamic force of the jet is as the effective head acting upon 
it, the loss of .505 of 7i is a matter of importance, espe¬ 
cially in cases of short pipes. 

The theoretical velocity being = -gjg? fh e theoretical 

1 

energy of the jet, under the same assumed conditions, is 



x Q x w = 321250 foot pounds per second = 584.09 
15 


/ 







226 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE. 


HP.; to representing tlie weight in pounds (= 62.34) per 
cubic foot of the water, and Q the volume or quantity of 
water in cubic feet per second. 

The energy E, due to v, is expressed by the equation, 

E = ■£- x Q x w (2) 


= 213631.2 foot pounds per second = 388.42 HP. 

The loss of energy from the quantity of water Q during 
the efflux in one second, being proportionate to the loss of 
head, is, 




v 


— 1 x Qw- 



107618.75 foot pounds per second = 195.67 HP. 

250. Ratio of Resistance at Entrance to a Pipe. 

—The ratio, .505, of h' to 7i, is very nearly a mean for tubes 
whose edges are square and flush in a plane partition. If 
the entrance of the tube is well rounded in' trumpet-mouth 
form, corresponding to the form of the rend contractd , the 
coefficient of velocity c v will be increased to about .98, and the 


ratio of resistance will become 



= .0412, equal in 


this case (Fig. 35) to about four feet head, and the head 
that can be made available for work will equal ninety-six 
feet. 

The disadvantage of the square edges, as respects both 
volume and dynamic force, is apparent. This resistance of 
entry of the jet into a tube, whose ratio of head we have 
determined, is force, or its equivalent head irrecoverably 
lost. Its maximum for a given head occurs when the tube 
is about three diameters loyg, the velocity being then at its 
maximum, and thereafter its value is reduced as the pipe is 
lengthened, and with the square of the velocity. 




COEFFICIENTS OF EFFLUX FROM PIPES. 


227 


RESISTANCE TO FLOW WITHIN A PIPE. 

251. Resistance of Pipe-wall. —We have heretofore 
considered the whole head H as applied to and entirely 
utilized in overcoming the resistance of entry of the jet into 
the pipe, and in generating the velocity among the'particles 
of the jet. 

We will now consider the resistances within the pipe and 
its appendages, and the portion of the velocity that must he 
converted into hydraulic pressure to overcome them. 

252. Conversion of Velocity into Pressure.—If 
the pipe P, Fig. 35, of three diameters length, he extended 
as at P\ a new resistance arising within the added length 
acts upon the jet and again reduces the volume of flow. A 
portion of the velocity of the jet is converted into working 
or hydraulic force, and is applied to overcome the resistances 
presented within the pipe, and the proportion of the velocity 
thus consumed is almost directly proportional to the length 
added of the pipe, of the given diameter. 

25.3. Coefficients of Efflux from Pipes. —The effects 
upon the volume of discharge through a given pipe conse¬ 
quent upon varying its length will he apparent upon inspec¬ 
tion of a table of coefficients of efflux, c , due to its several 
lengths respectively. 

We will assume the pipe to he one foot diameter, of 
clean cast iron, when the coefficients determined experi¬ 
mentally have mean values about as follows: 


TABLE No. SI. 

Coefficients of Efflux ( c ) for Short Pipes. 


Lengths, in diameters .. 

X 

5 

IO 

25 

5 ° 

75 

100 125 

150 

175 

200 

225 

250 

275 

300 

Coefficients (<:)• . 

.62 

.792 

.770 

• 7 i 4 

■643 

00 

00 

10 

.548.512 

• 485 

.462 

.440 

.420 

• 405 

.386 

•378 





































228 


FLOW OF WATER THROUGH PIPES. 


Plotted as ordinates, beginning with the theoretical 
coefficient, unity, they range themselves as in Fig. 36. 


Fig. 36. 



254. Reactions from the Pipe-wall.—A fair sam¬ 
ple of ordinary pipe casting, a cement-lined, lead, or glazed 
earthenware pipe are each termed smooth pipes, but a good 
magnifying lens reveals upon their surfaces innumerable 
cavities and projections. 

The molecules of water are so minute that many thou¬ 
sands of them might be projected against and react from a 
single one of those innumerable projections, even though it 
was inappreciable to the touch, or invisible to the naked 
eye. 

A series of continual reactions and deflections, originated 
by the roughness of the pipe, act upon the individual 
molecules as they are impelled forward by gravity, and 
materially retard * their How. 

In a given pipe, having a uniform character of surface, 
the sum of the reactions, for a given velocity, is directly as 

* The resistance was, by the earlier philosophers, attributed chiefly to the 
adhesion of the fluid particles to the sides of the pipe, and to the cohesion 
among the particles. Vide Downing, who accepts the views of Du Buat, D’Au- 
buisson, and other eminent authorities. Practical Hydraulics, p. 200. Lon¬ 
don, 1875. 












FORMULA OF RESISTANCE TO FLOW. 


229 


its wall surface, or as tlie product of the inner circumfer¬ 
ence into the length. Since in a pipe of uniform diameter 
the circumference is constant, the sum of the reactions is 
also directly as the length. 

The impulse of the flowing particles, and therefore their 
reactions and eddy influences, are theoretically proportional 
to the head to which their velocity is due, which is propor¬ 
tional to the square of the velocity, or, in general terms, the 
effective reactions are proportional nearly to the square of 
the velocity. 

The resistances arising from the interior surface of the 
pipe are, therefore, not only as the length , hut as the 
square 'of the velocity , nearly. 

The effect of the resistances is not equal upon all the 
particles in a section of the column of water, hut is greatest 
at the exterior and least at the centre, or, in a given section, 
approximately as its circumference divided l>y a function 
of its area* 

255. Origin of Formulas of Flow. —These simple 
hypotheses constitute the foundation of all the expressions 
of resistance to the flow of water in pipes, as they appear in 
the varied, ingenious, and elegant formulas of those emi¬ 
nent philosophers and liydraulicians who have investigated 
the subject scientifically. 

256. Formula of Resistance to Flow. —Place E to 
represent the sum of all the resistances arising from the 
circumference of the pipe (excluding those due to the entry); 
C for the contour or circumference of the pipe, in feet; JS for 
the section of the interior of the pipe, in square feet; l for 
the length of the pipe, in feet; and v for the mean velocity 

* The law of tlie effects of the resistances is believed to have been first for¬ 
mulated in the simple algebraic expressions now in general use, by M. Chezy, 
about the year 1775. 



230 


FLOW OF WATER THROUGH PIPES. 


of flow, in feet per second. Then the resistance to flow is 
expressed in equivalent head by the equation 

B = g!x l x (m)A. (4) 

257. Coefficient of Flow. —In the equation a new 
coefficient m appears, which also is to be determined by 
experiment. It is not to be confounded with the c hereto¬ 
fore investigated, but will hereafter be investigated inde¬ 
pendently. 

258. Opposition of Gravity and Reaction.—We 

have seen that gravity (§ 189) is the natural origin and the 
accelerating force that produces motion of water in pipes. 

Its effect, if no resistance was opposed, would be to con¬ 
tinually accelerate the flow. On the other hand, if its effect 
was removed, the resistances would bring the column to a 
state of rest. 

The two influences oppose each other continually, and 
therefore tend to the production of a rate of motion in which 
they balance each other. 

259. Conversion of Pressure into Mechanical 
Effect. —When the motion has become sensibly constant, 
a portion of the effect of gravity that appeared as velocity 
in the cases of orifices and short tubes, or its equivalent in 
the form of head is consumed by impact upon the rough 
projections of the pipe wall and reactions therefrom, and the 
remaining force due to gravity or head is producing the 
velocity of flow then remaining. 

2 GO. Measure of Resistance to Flow. —The effect 
of the resistance along a main pipe, when discharging 
water from a reservoir, as in Fig. 37, may be observed by 
attaching a series of pressure gauges at intervals, or by at¬ 
taching a series of open-topped pipes, as at p p x p 2 , etc. 


RESISTANCE INVERSELY. 


231 


\ 


Fig. 37. 



If tlie end / of the pipe is closed, water will stand in all 
the vertical pipes at the same level, ak , as in the reservoir. 

If the diameter of the pipe is uniform throughout its 
length, and the flow, the full capacity of the pipe, then 
water will stand in the several vertical pipes up to the in¬ 
clined line af ; provided that the top of p 2 he closed so that 
there may be a tendency to vacuum at n, and provided also 
that n is not more than thirty feet, or the height to which 
the pressure of the atmosphere can maintain the pipe full, 
above the line af\ at n'. 

When f is an open end discharging into air, and the 
vacuum at n is not maintained, a'n will be the total effec¬ 
tive head, and the portion of the pipe nf will be only parti¬ 
ally filled. 

261. Resistance Decreases as the Square of the 
Velocity.—If the discharge of the pipe is throttled at /, by 
a partial closing of a valve, by a contraction of the issue, or 
by diversion of the stream into other pipes of less capacity, 
and a portion of the velocity is in consequence converted 
into pressure equivalent to the head//, then the resistance 
will be lessened as the square of the velocity decreases, and 
water will stand in the vertical pipes, or the gauges will in¬ 
dicate the inclined line af. This is the usual condition of 
mains in public writer supplies. 



























232 


FLOW OF WATER THROUGH PIPES. 


262. Increase of Bursting 1 Pressure.—One effect of 
throttling the discharge is seen to be an increase of bursting 
pressure upon the pipes, which is greater when the exit is 
entirely closed than when there is a constant liow, and which 
decreases as the velocity increases, though a sudden clos¬ 
ing of a valve against a rapid current will probably prove 
disastrous to an ordinary pipe that is fully able to sustain 
a legitimate pressure due to the head. 

263. Acceleration and Resistance.—Let ctb (Fig. 38) 
be a vertical pipe discharging water from a reservoir A, 
maintained always full. If, before the water entered the 

Fig. 38 . 



pipe, a single particle had been dropped into its centre from 
a , the velocity of movement of the particle would, in conse¬ 
quence of the effect of gravity upon it, have been constantly 
accelerated through its whole passage along the axis. 






































DESIGNATION OP h" AND l. 


233 


Its velocity, when it had reached b, would have been 
equal to V2gH , when II represents the vertical height ab 
in feet. 

The greater the height ab the greater the sum of the ac¬ 
celerations by gravity, and also, if the pipe is flowing full , 
the greater the length a'b the greater the sum of the resist¬ 
ances acting upon the column of water to retard it. 

264. Equation of Head Required to Overcome 
the Resistance.—Let v be the velocity of the jet issuing 
from £>, h the head to which v is due, and 7i" the head act¬ 
ing upon the resistance i?, and m a coeflicient. 

Then the ratio of the amount of the force of gravity, or 
equivalent head, 7i", converted into hydraulic pressure to 
balance the resistances within the given length of pipe, and 
for the given head, is to the head, 7i , producing the velocity 


C 


v 4 




as ^ x Im x pr- to =r- ; 

S 2g 2g 


hence the equation of resistance 


head is 




x l x 

r 


mv 2 

~2g' 



265 . Designations of 71’ and l— In long pipes the 
total head, H— 7i + Ti + h". 

The head, or cTiarge of water Ti’ acting upon the resist¬ 
ances, is the vertical height of the surface of the reservoir, 
less the height aa" = Ti (Fig. 38), necessary to generate the 
velocity v, and also less the height a”a ' = 7i’ necessary to 
overcome the resistance of entry, above the centre of the 
discharging jet at the exit; or if the discharge is into 
another body of water, above the surface of the lower 

body. 

The length l to be taken, is the actual length of the axis 
of the pipe. 

In topographical surveys the chain is held horizontal, 




234 


FLOW OF WATER THROUGH PIPES. 


and the distance df is in plotting expressed by its projec- 

7i" 7cf 

tion a'k, but for pipes the true ratio -y is . 

i CLJ 

Then whatever the position or direction of the pipe a'b , 
or df, or if, or onf (abstracting for the present any resist¬ 
ance of curvature), the equation of h" measures the resistance 
unless, in the case of a pipe discharging near to its full capa¬ 
city, an upward curve, n, shall rise more than thirty feet 
above the line of hydraulic mean gradient df, when Id is 
to be taken in two sections, first from d to n vertically, and 
second from ntof vertically reduced by the effect of the 
vacuum, if any, or as a simple channel without pressure if 
the length nf does not fill. 

266. Variable Value of m. —In the equation of Id, (5), 
we have the coefficient m, whose several values are to be 
deduced from actual measurements of the flow of water 
through pipes, and whose governing conditions are to be 
closely observed and studied. 

The physical conditions of various pipes are so different 
that special coefficients are required for each class of con¬ 
ditions. 

A slight increase in the roughness of the interior surface 
of the pipe, occasional sudden enlargements or contractions 
of the diameter of the pipe, and sudden bends in the direc¬ 
tion of the pipe, may be instanced as sufficient departures 
from the conditions of straight pipes with uniform diameters 
and surfaces to materially modify the value of its coefficient 
of flow. 

267. Investigation of Values of m. —For the de¬ 
termination of a series or table of coefficients, m, for full 
pipes, we will select data from published tables of * exper- 

* Recherches experimentales relatives au movement de l’eau dans le 
tuyaux. Paris, 1857. 




DEFINITION OF SYMBOLS. 


235 


iments by Henry Darcy, made while he was director of the 
public water service ot the city of Paris ; from* experiments 
by Gfeo. S. Greene, made while chief engineer of the Croton 
Aqueduct Department of New York city ; from experiments 
by Geo. H. Bailey, Esq., made while chief engineer of the 
Jersey City Water-works ; from some of the famous exper¬ 
iments of Du Buat, Couplet, and Bossut, which furnished 
the chief data for the elegant formulas of those eminent 
philosophers, as well as those of Pronyf and Eytelwein, 
and from several other sources. 

268. Definition of Symbols. —By transposition we 
have 

O s h» 1 

m = 2 g x c x t x i? (7) 

7i n 

The member y is the ratio of the height which the par¬ 
ticles fall through in the given length, equal or the 

sine of the angle of inclination haf, Fig. 38. The inclina¬ 
tion af is termed the “slope” or the hydraulic mean gra¬ 
dient , and is usually designated by the letter i. The point 
a' is always beneath the surface of the water a depth aa) 
necessary to generate the velocity v in the pipe, and to 
overcome the resistance of entry, whether the pipe be in the 
position af, if, or onf. 

The depth aa) varies as the velocity varies, and the 
“slope” i corresponds to an imaginary right line connect¬ 
ing the points a 1 and f. 

a 

The member as now inverted (§ 256) refers to the 
ratio of the section to the contour of the given pipe, or to the 

* Descriptive Memoir of the Brooklyn Water-works, by James P. Kirk¬ 
wood. Van Nostrand, N. Y., 1867. 

f Vide Recherches Physico-Matliematiques sur la Tkeorie du Mouvement 
des Eaux Courantes, 1804. 




236 


FLOW OF WATER THROUGH PIPES. 


sectional area . , , ,, ,, 7 . ,, 

—=-.——. it is termed the “ mean radius , or, in 

wetted perimeter 

the cases of pipes and channels partially tilled, the hydrau¬ 
lic mean depth, and is usually designated by the letter r. 
The value of r for full pipes is always equal to one-fourth 

d 

of the diameter = -, according to well-known properties of 
the circle. 

269. Experimental Values of the Coefficient of 

Flow. —We have then, as an equivalent for equation (7): 


m = 


2 gri 


v 


2 5 


2 gh"S 

or m — 

Civ 2 


( 8 ) 


TABLE No. 52a. 


2a dh 
m = -r^-o x 


4v 2 


l 


Experimental Coefficients ( m ) of Flow of Water in 
CLEAN Pipes, under Pressure. 

Experiments by Hamilton Smith, Jr., (Sheet-iron Asphaltum-coated Pipes,) 
at North Bloomfield, California, where 2 g = 64.29. 


Diameter = d 
in feet. 

Head = h , 
in feet. 

Length = /, 
in feet. 

Velocity = v , 
in feet per sec. 

Coefficient = m. 

.911 

22.650 

684.8 

IO.048 

.00479 

.911 

17.832 

697.0 

8.685 

.00496 

.911 

12.098 

7 I 3.9 

6.952 

.00518 

.911 

9.618 

721.3 

6.115 

.00520 

.911 

6.203 

730.6 

4-755 

.00554 

I.056 

22.711 

684.9 

10-755 

.00486 

I.056 

15.519 

699.6 

8.679 

.00499 

I.056 

IOI27 

709.2 

6.982 

•00495 

I.056 

4-799 

718.4 

4.612 

.00532 

I.230 

22.036 

684.4 

12.302 

.00419 

I.230 

17.132 

6 q5-6 

IO.750 

.00421 

I.230 

n.592 

705.0 

8 . 5 I 7 

.00446 

1-230 

8.713 

710.7 

7-334 

.00450 

I.23O 

7-813 

712.4 

6.861 

.00459 

I.230 

3.614 

719.9 

4 A 98 

.00511 

I.416 

296.1 

4438.7 

20.130 

.00373 



















EXPERIMENTAL COEFFICIENTS. 


237 


TABLE No. 3 2 . 

Experimental Coefficients (m) of Flow of Water in C/ean 
Pipes, under Pressure, m = = 2 —~ x —, 

( /‘i)* 


V A 


V ' 


EXPERIMENTS BY H. DARCY (Cast-iron Pipes). 


Diameter = d , 
in feet. 

Head = h '\ 
in feet. 

Length = /, 
in feet. 

V elocity = z/, 
in feet per sec. 

Coefficient = in . 

O.2687 

O.066 

328.09 

O.2885 

.OIO4478 

a 

I.742 

a 

L8399 

.0067800 

a 

3-347 

a 

2.5946 

.0065508 

a 

13.260 

a 

5 -I 509 

.0065850 

a 

39.299 

a 

8.9242 

.0065162 

a 

56.011 

a 

IO.7II5 

.0064320 

O.45 01 

0.079 

328.09 

O.4887 

•OO73054 

a 

.686 

a 

1.602 I 

.0059026 

a 

i-S 5 8 

a 

2.5021 

.0054960 

a 

54-975 

a 

I 5 - 39 2 9 

.005I240 

O.6151 

O.089 

328.09 

O.6544 

.0062884 

a 

1.207 

a 

2.499 1 

.0058476 

a 

2.64I 

Si 

3-7155 

.0057898 

a 

4-369 

a 

4.9045 

.0055296 

a 

12. 500 

te 

8.2564 

.0055482 

Si 

f'- 

100 

• 

a 

16.2360 

.0054948 

0 - 975 1 

O.O92 

328.09 

O.7997 

.0068802 

u 

.883 

a 

2.7134 

.0057306 

a 

I.762 

a 

3-7863 

.0058728 

a 

3-625 

a 

5-4039 

•OO59314 

a 

7.562 

a 

7-8330 

.0058890 

a 

13-473 

a 

1 °-35 7 5 

.O060OIO 

I.6427 

O. 148 

328.09 

I -3765 

.0062950 

a 

.148 

a 

I.4685 

•OO553IO 

a 

.197 

a 

1-5549 

.0065688 

a 

•394 

a 

2-5954 

.0047160 

tc 

.853 

a 

3.6637 

.0051216 

a 

.820 

a 

3.6900 

.OO48536 
















238 


FLOW OF WATER THROUGH PIPES. 


TABLE No. S 3 . 


Experimental Coefficients (m) of Flow of Water in Clean 

2 g/i'S 2 gri 

CW~ 


Pipes, under Pressure, m — 


EXPERIMENTS BY THE WRITER (Wrought-ipon Cement-lined 

Pipe). 


Diameter = d , 
in feet. 

Head = h>\ 
in feet. 

Length = /, 
in feet. 

Velocity = v. 
in feet per sec. 

Coefficient = m. 

I.6667 

1.86 

8171.O 

O.949 

.006785 

a 

3.60 

a 

I.488 

•OO5338 

<{ 

5-93 

a 

I.925 

•OO5254 

a 

8.48 

a 

2.329 

•OO5133 

a 

IO -93 

a 

2.598 

•OO53I7 

a 

12.91 

a 

2.867 

•005157 

a 

16.28 

a 

3.271 

.004996 

tc 

18.60 

a 

3*439 

•005163 

a 

22.22 

a 

3 * 74 i 

•OO5213 


24*54 

cc 

3.920 

•OO5243 

a 

2 5 * 5 8 

it 

4.00 

•OO5249 

a 

26.16 

(C 

4.04 

.005262 


TABLE No. 84. 

EXPERIMENTS BY DU BUAT (Tin Pipes). 


O.0889 

•973 

10.401 

5 1 7 9 

.004992 

it 

1.484 

10.401 

6*334 

.005089 

a 

.0481 

12.304 

0.7717 

•009393 

a 

•375 

12.304 

2.606 

.006424 

a 

1.220 

12.304 

5.220 

.005 207 

a 

•013 

^ 5-457 

0.1411 

.014276 

a 

1.022 

a 

i *775 

.007091 

a 

I *954 

a 

2.546 

.006585 


TABLE No. 36. 

EXPERIMENTS BY BOSSUT (Tin Pipes). 


0.0889 

0.331 

53*284 

1.085 

.001698 

a 

.976 

86.094 

T979 

.004142 

.11841 

. 864 

31-956 

2-945 

•005943 

a 

2.066 

191.840 

1.679 

.007282 

u 

I.699 

31-956 

4.308 

.005461 

.178 

• 765 

31-956 

3-581 

•005363 

a 

2.OI9 

191.840 

2.196 

.006270 

a 

I.892 

95 - 9°5 

2.250 

.011190 

a 

1.49 1 

3!*95 6 

5-230 

.004901 






















EXPERIMENTAL COEFFICIENTS. 


239 


TABLE No. 56. 


Experimental Coefficients (m) of Flow of Water in Clean 


Pipes, under Pressure. 


m — 


2gfl"S 
Civ 1 ' 


EXPERIMENTS BY COUPLET (Iron Pipes). 


Diaameter = d , 
in feet. 

Head = h'\ 
in feet, 

Length = /, 
in feet. 

Velocity = v , 
in feet per sec. 

Coefficient = m 

0.4439 

O.492 

7481.88 

O.1785 

.OOI475 

a 

I.005 

7481.88 

.2802 

.012230 

•4374 

I.484 

7481.88 

•3 6 65 

.OIO390 


I.670 

« 

.4258 

.008667 

a 

2.130 

(( 

.4640 

.009309 

(( 

2.215 

a 

.4728 

.OO9323 

I.5988 

12.629 

3836.66 

3-4779 

.007004 


T 

ABLE No. 57. 


EXPERIMENTS BY W. A. 

PROVIS. (Lead Pipes.) 

O.I25 

2.91666 

20.00 

6.1495 

.006465 

(( 

a 

40.00 

4.7588 

.005398 

(C 

a 

60.00 

3.9032 

.005360 

a 

a 

80.00 

3-39 61 

.005287 

(6 

(( 

100.00 

3.0897 

.OO5122 


TABLE No. 58. 

EXPERIMENTS BY RENNIE. 

With glass pipes slightly rounded at the ends. 


O.OO20833 

1.0 

1.0 

7.1627 

.000653 

a 

2 

a 

IO.4196 

.000408 

(( 

3 

a 

12.9409 

.000601 

(< 

4 

a 

14.6240 

.000627 

.OO41666 

1.0 

1.0 

5-645 0 

O 

w 

O 

O 

• 

a 

2 

a 

8.3676 

.OOI916 

(C 

3 

(( 

IO.0497 

.OOI992 

a 

4 

(( 

11.6000 

.OOI994 

.00625 

1.0 

1.0 

5-5487 

.OO4162 

a 

2 

(( 

8.1852 

.00481 4 

<( 

3 

(( 

9-8551 

.003956 

a 

4 

(( 

IO.8320 

.004378 

rf 

OO 

O 

O 

• 

1.0 

1.0 

6.1028 

.004584 

(( 

2 

(( 

8.5386 

.004684 

e* 

3 

a 

IO.8003 

.004392 

cs 

4 

a 

13.0400 

.004016 
























240 


FLOW OF WATER THROUGH PIPES. 


TAB L E No. 59. 

Experimental Coefficients ( m ) of Flow of Water in Old 

2 gti'S 

Pipes, under Pressure, m = - • 


EXPERIMENTS BY H. DARCY. (Foul Iron Pipes.) 


Diameter = d , 
in feet. 

Head = A", 
in feet, 

Length = /, 
in feet. 

Velocity = v , 
in feet per sec. 

Coefficient = m . 

O.II94 

O.223 

328.09 

O.2669 

.018342 

a 

.600 

u 

•4273 

.OI92IO 

(( 

2.198 

(< 

.8291 

•018735 

<< 

5-°°3 

(C 

I.2494 

.018784 

(( 

10.630 

<( 

I.8079 

.OI9055 

i ( 

13.632 

(( 

2.0772 

.018511 

O.2628 

O.213 

328.09 

O.4040 

.Ol68lI 

a 

.820 

a 

.8242 

•OI 555 I 

a 

2 -379 

<e 

I.4645 

.OI4288 

(( 

5.282 

a 

2.2226 

.OI3774 

<< 

10.171 

(( 

3 -° 5 I 7 

.OI4082 

<( 

14.879 

(< 

3*7434 

.OI3679 

O.8028 

0.308 

328.09 

1.0080 

.OII934 

(S 

.663 

(< 

1.4824 

.OI1878 

a 

i- 55 2 

<c 

2.3218 

•011334 

(< 

3*773 

<< 

3.6283 

.011285 


7 * 5 1 3 

<( 

5.0727 

.OI I494 

« 

10.499 

a 

6.0169 

.OII417 

(< 

13.468 

t ( 

6.8037 

.OII454 

1 ( 

0 

00 

ro 

<e 

12.5779 

.OII415 


TABLE No. 60. 

EXPERIMENT BY GEN. GEO. S. GREENE, C. E., 

Upon a New York City cast-iron Main. (Tuberculated.) 

?.0 | 20.215 | 11217.00 | 2.99967 | .00966 


16667 


EXPERIMENT BY GEO. H. BAILEY, C. E., 

Upon a Jersey City cast-iron Main. (Tuberculated.) 


28.1285 I 29715.00 


1 -43795 


.01228 

















EXPERIMENTAL COEFFICIENTS. 


241 


TABLE 60 .—(Continued.) 


Experimental Coefficients (m) of Flow of Water in Old 

2 gh"S 


Pipes, under Pressure, m — 


Civ ' 3 * 


EXPERIMENT UPON THE COLINTON MAIN.* 


Eight years in use. 


Diameter = d , 
in feet. 

Head = h", 
in feet. 

Length = /, 
in feet. 

Velocity = v, 
in feet per sec. 

Coefficient -- m. 

1-3334 

184 

3815 

I 4-5°° 

.OO4923 

66 

230 

25765 

5-25 2 

•OO5556 

66 

420 

2958° 

6.816 

.006559 


LAMBETH WATER WORKS MAIN. 


2-5 

25 

54120 

1.772 

.005918 

i-5 8 3 

41 

2 2440 

2-734 

.006229 

1 

3 8 

5200 

4-353 

.006208 


LIVERPOOL WATER 

WORKS MAIN. 

1 

i 27 

8140 

2.644 

| .OO7633 


CARLISLE WATER 

WORKS MAIN. 

* 

34-5 

6600 

3-568 

.006610 


EXPERIMENTS BY THE WRITER. 


With unlined wrought iron pipe (gas tubing), the jet entering through a stop¬ 
cock and piston meter, with coefficient c — .58 when length — 0.25. The 
pipe had been in use one week, but had rusted considerably. 


O.08334 

28.73 

0.25 

46.70 

• • • * 

6 6 

85.57 

9 

18.964 

.035467 

<6 

9 8 -34 

735 

4.850 

.007636 

66 

96.38 

1337 

3-538 

.007722 

66 

87-33 

2040 

2.722 

.007746 


* Vide Proceedings of Inst. Civ. Engineers, p. 4, Feb. Gtli, 1855, London. 


16 

























242 


FLOW OF WATER THROUGH PIPES. 


TABLE No. 6 1. 

Series of Coefficients of Flow ( m ) of Water in Clean Pipes, 
under Pressure, at Different Velocities, and in Pipes 

of Different Diameters, (m = 2< ^—— = 

\ Civ 1 v 2 / 



Diameters. 

Velocity. 

X inch. 

%!' 

1" 

i 1 /*" 


2 h 


.0417//. 

.0625'. 

•0834'. 

.1250'. 

. 1458 '. 

.1667'. 

Feet per 
Second. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

.1 

O.OI50 

O.OI30 

0.0119 

0.0107 

O.OO970 

O.O0870 

.2 

.OI43 

.0126 

.OI l6 

.OI05 

.OO952 

.00860 

•3 

• OI 37 

.0123 

.OII3 

.OIO3 

.OO937 

.00850 

•4 

• OI 33 

.OII9 

.OI IO 

• OIOO 

.OO92O 

.O084O 

•5 

.0128 

.OI l6 

.OIO7 

.OO984 

.OO904 

.00830 

.6 

.0124 

.OII3 

I .OIO4 

.OO960 

.00890 

.00822 

•7 

.0120 

.OIII 

.0102 

.OO940 

.00873 

.00813 

.8 

.0116 

.0108 

.OIOO 

.OO922 

.00860 

.00804 

•9 

.0113 

.OIO5 

.OO972 

.OO9IO 

.00850 

.OO798 

1.0 

.0110 

.0102 

.OO950 

.00893 

.00840 

.OO79O 

1.1 

.0107 

•OO995 

.00933 

.00880 

.00826 

.OO783 

1.2 

.0104 

.00973 

.OO913 

.00867 

.00817 

.OO776 

!-3 

.0101 

.OO952 

.00898 

.00854 

.00809 

.00770 

1.4 

.00992 

.OO93O 

.00882 

.00843 

.00800 

.OO763 

1-5 

.00959 

.OO91O 

.00868 

.00832 

•00793 

.OO757 

r.6 

.00942 

.OO89O 

.00854 

.00823 

.OO786 

.OO75O 

I -7 

.00920 

.0087 2 

.00840 

.00814 

.OO777 

.OO746 

i.8 

.00900 

.00856 

.00830 

.00806 

.OO769 

.OO74I 

i*9 

.00880 

.00842 

.00820 

.00800 

.OO763 

.OO736 

2.0 

.00862 

.00830 

.008l0 

.OO79O 

•00757 

.OO73I 

2.25 

.00840 

.00804 

.OO785 

.OO770 

.OO742 

.OO72I 

2 *5 

.00795 

.00780 

.OO768 

.OO752 

.OO73O 

.007 IO 

2 -75 

.00775 

.OO761 

.OO75O 

.OO736 

.OO716 

.00700 

3 -o 

.00753 

.OO745 

.OO734 

.OO722 

.OO707 

.00692 

3-5 

•00732 

.OO722 

.00712 

.00702 

.00692 

.00680 

4 

.00722 

.007IO 

.00702 

.00692 

.00682 

.O067I 

5 

.00704 

.00693 

.00684 

.00675 

.00664 

.00654 

6 

.00689 

.00678 

.00670 

.00660 

.00650 

.O064O 

7 

•00675 

.00664 

.00657 

.00648 

.00639 

.00629 

8 

.00663 

.00652 

.00646 

.00638 

.00627 

.006l8 

9 

.00652 

.00643 

.00636 

.00628 

.00618 

.00609 

10 

.00644 

.00634 

.OO628 

.00620 

.00610 

.00601 

12 

.00630 

.00620 

.00614 

.00607 

.OO599 

.00590 

14 

.00622 

.00613 

.00606 

.00600 

.OO592 

.OO584 

16 

.00618 

.00608 

.00600 

•°°595 

.OO589 

.OO581 

18 

.00616 

.00606 

.OO599 

.OO594 

.OO588 

.OO580 

20 

.00615 

.00605 

.OO598 

•00593 

.OO587 

.00579 














































COEFFICIENTS OF FLOW OF WATER. 


243 


TABLE No. 61 — (Continued). 

Coefficients of Flow ( m ) of Water in Clean Iron Pipes 

under Pressure. 


Diameters. 


6 " 

• 5 '- 


Coefficient. 


8 " 

.6667'. 


Coefficient. 


Velocity 



Coefficient. 


Feet per 
Second. 


•3 

•4 

•5 

.6 

•7 

.8 

•9 

1.0 

1.1 

1.2 
i-3 
1.4 

1- 5 

1.6 

1 • 7 

1.8 

1.9 
2. 

2.25 

2.50 

2 - 75 

3- 

3- 5 

4- 

5 - 
6. 

7- 

8 . 

9- 

10. 

12. 

14. 

16. 

18. 

20. 


0x0800 
.00792 
.00784 
.00780 
.00774 
.00767 
.00760 
.00754 
.00750 
.00743 
.00739 
.00733 
.00729 
.00724 
.00720 
.00716 
.00712 
.00708 
.00703 
.00700 
.00690 
.00683 
.00675 
.00670 
.00660 
.00651 
.00636 
.00622 
.00610 
.00600 

.00593 

.00585 

.00582 

.00573 

.00570 

.00568 

.00566 


4" 

• 3333 '- 


Coefficient. 

O.OO763 

.00755 

.00750 

.OO742 

.OO737 

.OO732 

.00727 

.OO722 

.00718 

.OO712 

.00708 

.00704 

.00700 

.OO697 

.00693 

.00690 

.00687 

.00684 

.00680 

.00678 

.00670 

.00662 

.00655 

.00650 

.00640 

.00631 

.00618 

.00605 

•00595 

.OO587 

.00578 

.OO572 

.00560 

•OO554 

•OO552 

.OO550 

.OO549 


O.OO73O 

.00724 

.00720 

.OO713 

.00708 

.00702 

.00697 

.00693 

.00688 

.00684 

.00679 

.00674 

.00670 

.00666 

.00662 

.00658 

.00655 

.00652 

.00650 

.00648 

.00640 

.00634 

.00629 

.00623 

.00614 

.00607 

.00594 

.00582 

.00572 

.OO562 

.00555 

•OO549 

.00540 

•00533 

•00530 

.OO528 

•OO525 


O.OO704 
.00698 
.00693 
.00688 
.00682 
.00677 
•00673 
.00668 
.00663 
.00659 
.00654 
.00652 
.00648 
.00644 
.00640 
•00637 
•00633 
.00630 
.00628 
.00624 
.00617 
.oofti I 
.00605 
.00600 
.00593 
.OO586 
.00573 
.OO562 
.00552 

.00544 
.OO538 
•OO53O 
.00522 
.005 l6 
.00513 
.005 IO 

.OO508 


10" 

.8333'. 


Coefficient . 

O.O0684 
.00678 
.00673 
.00668 
.00663 
.00659 
.00654 
.0065 I 
.C0648 
.00643 
.00640 
.00635 
.00632 
.00628 
.00625 
.00622 
.00618 
.00615 
.00612 
.00609 
.00603 
.00596 

.OO59O 

.00584 

.00574 

.00568 

.00558 

.00548 

.00540 

.OO532 

.00525 

.00520 

.OO512 

.OO507 

.00502 

.OO50O 

.OO498 


1.o'. 


Coefficient. 

O.O0669 
.00662 
.00657 
.00652 
.00648 
.00642 
.00638 
.00633 
.00629 
.00624 
.00620 
.00617 
.00613 

.Oo6lO 

.00607 

.00603 

.00601 

.OO599 

.OO597 

•00593 

.00588 

.00581 

•00575 

•00570 

.00561 

•00553 

•OO543 

•00534 

•OO527 

.00520 

.00512 

.00508 

.OO50O 

.00494 

.OO49I 

.OO488 

.OO485 









































244 


FLOW OF WATER THROUGH PIPES. 


TABLE No. 6 1—(Continued). 

Coefficients of Flow ( m ) of Water in Clean Cast-Iron 

Pipes under Pressure. 


Velocity. 

Diameters. 

14 inches 

16" 

18" 

120" 

24" 

27" 



1.1667 feet. 

I- 3333 '- 

i. 5 '. 

1.6667'. 

2.0'. 

2.25'. 

Feet per 
Second . 

Coefficient . 

Coefficient . 

Coefficient . 

Coefficient . 

Coefficient . 

Coefficient . 

. I 

0.00650 

0.00623 

% • • • 

• • • • 

• • • • 

• • • • 

. 2 

.00644 

.00619 

0.00600 

O.OO583 

• • • • 

• • • • 

•3 

.00640 

.00614 

.00597 

•OO578 

O.OO548 

O.OO53O 

' 4 

.00634 

.006II 

.OO592 

.00574 

.00544 

.OO526 

•5 

.00630 

.00607 

.00588 

•00570 

.00540 

•OO523 

.6 

.00625 

.00603 

.00584 

.OO567 

•00537 

.OO52O 

•7 

.0062I 

.00600 

.00580 

•OO563 

•00533 

•OO517 

. 8 

.00617 

•00597 

.00577 

.OO561 

•OO531 

•OO513 

•9 

.00612 

•OO593 

•00573 

•OO558 

.00528 

.OO5II 

I .o 

.00609 

.00588 

.00570 

•00555 

.00525 

.OO508 

i. i 

.00605 

.OO584 

.00568 

•OO552 

.00522 

•OO505 

I . 2 

.00601 

.00581 

.00564 

•OO550 

.00520 

•OO503 

1 -3 

.00598 

.OO578 

.OO561 

.00548 

.00517 

.OO50O 

1.4 

•OO593 

.00575 

•00559 

•OO545 

.00514 

.OO498 

i *5 

.00590 

.00572 

•OO556 

.OO542 

.00512 

•OO495 

1 • 6 

.00587 

.00569 

•00553 

•00539 

.00510 

•OO493 

i *7 

.00584 

.00566 

•00551 

•OO536 

.00508 

.OO49I 

1.8 

.00582 

.00563 

•OO549 

•OO534 

.00506 

.OO489 

1.9 

.00579 

.00561 

.00546 

•00532 

.00503 

.OO487 

2.0 

.00576 

.OO559 

•OO543 

.OO529 

.00501 

.OO485 

2.25 

.00570 

.00553 

•OO538 

•OO524 

.00497 

.OO480 

2.50 

.00564 

.00548 

•00533 

.OO518 

.00492 

•00475 

2 -75 

•00559 

.OO543 

.00528 

•OO513 

.00488 

.OO472 

3 - 

•OO554 

.OO538 

•OO523 

.OO509 

.00483 

.OO468 

3-5 

•00547 

.OO529 

.00516 

.00502 

.00478 

.OO462 

4 - 

.00540 

.OO524 

.00511 

.OO498 

•00473 

.OO458 

5 - 

•OO530 

•OO515 

.00501 

.OO49O 

.00466 

•00451 

6. 

.00520 

.OO507 

•OO495 

.OO482 

.00460 

.OO446 

7 - 

.00512 

.00500 

.00489 

.OO476 

•00453 

.OO44O 

8. 

.00503 

.OO49I 

.00483 

.00470 

.00450 

•00435 

9 - 

.00498 

.OO489 

.00478 

.OO466 

•OO445 

•OO43I 

10. 

•OO493 

.OO483 

.OO473 

.00462 

•OO443 

.OO429 

12. 

.00487 

.OO478 

.00468 

.OO457 

.00440 

.OO429 

14. 

.00482 

•OO473 

.00463 

.OO452 

•OO434 

.00422 

16. 

.00480 

.00470 

.00460 

.00450 

.OO432 

.00420 











































COEFFICIENTS OF FLOW OF WATER. 


245 


TABLE No. 61—(Continued). 

Coefficients of Flow ( m ) of Water in Clean Cast-Iron 
Pipes, or Smooth Masonry, under Pressure. 



Diameters. 

Velocity. 

30 inch 

33 " 

36" 

40" 

44 " 

4 °" 


2.5' feet. 

2.75'. 

3.0'. 

3.3333'. 

3.6667''. 

4.0'. 

Feet per 
Second. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

•4 

O.OO5 IO 

O.OO497 

O.OO476 

• • • • 

• • • • 

• • • 

•5 

.00507 

.OO492 

.OO473 

O.OO436 

O.OO42O 

O.OO4OO 

. 6 

.OO504 

.OO49O 

.0047I 

•OO434 

.OO418 

.OO399 

•7 

.OO50I 

.OO488 

.OO469 

.00432 

.OO416 

.OO398 

.8 

.OO498 

.00485 

.00467 

.OO43I 

.OO414 

.OO397 

•9 

.OO495 

.OO482 

.00464 

.OO430 

.00412 

.OO396 

I . o 

.OO492 

.00480 

.OO462 

.OO428 

.OO4I I 

•OO395 

i. i 

.OO49O 

.OO478 

.OO459 

.OO426 

.OO4IO 

.OO394 

I . 2 

.OO488 

.OO475 

.OO457 

.OO424 

.OO409 

.OO393 

i -3 

.OO486 

.OO472 

.OO455 

.OO423 

.OO407 

.OO392 

1.4 

.OO484 

.OO470 

.OO453 

.OO422 

.OO406 

.OO39I 

i 5 

.OO482 

.OO468 

.OO45I 

.OO42I 

.OO4O4 

.OO39O 

i 6 

.OO480 

.OO466 

.OO450 

.OO42O 

.O0403 

.OO388 

i -7 

.OO477 

.00464 

.OO448 

.OO419 

.00402 

.OO387 

i.8 

.OO475 

.00462 

.OO446 

.OO418 

.OO4OI 

.OC386 

1.9 

.OO473 

.OO460 

.OO444 

.OO417 

.OO40O 

.OO385 

2. 

.OO47O 

.OO458 

.OO442 

.OO416 

.OO399 

.00384 

2.25 

.OO465 

.OO453 

•OO437 

.OO413 

.CO397 

.OO382 

2-5 

.00460 

.OO449 

.OO432 

.OO4IO 

.OO394 

.00380 

2.75 

.OO456 

.OO444 

.OO428 

.00408 

.OO39 1 

.CO378 

3 - 

.OO452 

.OO44O 

.OO424 

.00407 

.OO389 

.OO376 

3-5 

.OO446 

.OO434 

.OO419 

.OO4O2 

.00386 

.OO373 

4 - 

.OO44I 

.OO43O 

.OO415 

.OO4OO 

.O0383 

.OO370 

5 - 

.OO436 

.OO423 

.OO41O 

•00395 

.OO381 

.00366 

6. 

.OO43O 

.OO418 

.OO405 

.OO39I 

.OO377 

.OO363 

7 - 

.OO427 

.OO413 

.00401 

.OO388 

.00373 

.00361 

8. 

.00422 

.OO4IO 

.OO398 

.OO384 

•OO37I 

.OO358 

9 - 

.OO418 

.00407 

.00395 

.OO382 

.OO37O 

•°°355 

10. 

.OO415 

.00404 

.OO392 

.00380 

.OO367 

•00353 

12. 

.OO4I2 

.OO40O 

.OO389 

.OO377 

.OO364 

•00351 

14. 

.OO409 

.OO397 

.OO386 

.OO373 

.OO363 

.00350 

16 . 

.OO406 

•00395 

•OO383 

.OO370 

.OO360 

.00347 



























246 


FLOW OF WATER THROUGH PIPES. 


TABLE No. 61—(Continued). 

Coefficients of Flow ( m ) of Water in Clean Cast-iron Pipes 
or Smooth Masonry, under Pressure. 



Diameters. 

Velocity. 

54 inches. 

60" 

72" 

84" 

96" 


4.5 feet. 

5 -o'. 

6.o r . 

7.0'. 

8.o r . 

Feet per second. 

• 4 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

Coefficient. 

'T 

•5 

O.OO378 

O.OO358 

O.OO339 

O.OO318 

O.OO29O 

.6 

.00377 

•00357 

•OO338 

.OO317 

.00289 

•7 

.OO376 

.OO356 

•°°337 

•OO317 

.00288 

.8 

•°°375 

•00355 

•00336 

.OO316 

.OO287 

•9 

.00374 

•00354 

•°°335 

•OO315 

.00286 

1.0 

.00373 

•00353 

•00334 

•OO314 

.00286 

1.1 

.00372 

•OO352 

•00333 

•OO313 

.OO285 

1.2 

.00371 

•OO35I 

•00332 

•OO313 

.OO285 

1-3 

.00370 

•00350 

•00332 

.OO312 

.00285 

1.4 

.00369 

•OO350 

•00331 

.OO312 

.OO284 


.00368 

•OO349 

•00331 

.OO31 I 

.00284 

i.6 

.00368 

.OO348 

•00330 

.OO3II 

.OO284 

I -7 

.00367 

•OO347 

.00329 

.OO31O 

.OO283 

i.8 

.00366 

•OO347 

.00329 

.OO309 

.OO283 

i -9 

.00365 

.OO346 

.00328 

.OO309 

.OO283 

2 

.00364 

.OO346 

.00328 

.00308 

.00282 

2.25 

.00362 

•OO344 

.00327 

•OO307 

.00282 

2-5 

.00360 

.OO342 

.00325 

.00306 

.00281 

2-75 

.00358 

.OO34I 

•00323 

.OO305 

.00280 

3 

•oo 357 

•OO339 

.00321 

.00302 

.OO278 

3-5 

•00353 

•°°337 

.00320 

.OO3OO 

.OO276 

4 

.00350 

•00333 

.00318 

.OO298 

.OO274 

5 

•oo 345 

.00329 

•0031.3 

.OO294 

.OO272 

6 

.00340 

.00324 

.00310 

.OO292 

.00268 

7 

•00338 

.00322 

.00308 

.OO289 

.00266 

8 

•00335 

.00320 

.00304 

.00286 

.OO264 

9 

•00332 

.00318 

.00302 

.OO283 

.00262 

10 

•00331 

.00316 

.00300 

.00282 

.00261 

12 

•00330 

•00313 

.00299 

.00280 

.00260 

14 

.00329 

.00312 

.00298 

.OO279 

.OO259 






























EFFECTS OF TUBERCLES. 


247 


270. Peculiarities of the Coefficient (m) of Flow.— 

In the tables and diagram of coefficients (m) of flow in pipes, 
as well as in those of coefficients of discharge (c) through 
orifices, there is variation in value with each variation in 
velocity of the jet. In the case of pipes, there is also a 
variation with the variation of diameter of jet, that equally 
demands attention. 

It will be observed in the tables of experiment above 
quoted that the coefficient decreases as the diameter or 
hydraulic mean radius increases, and also that with a 
given diameter the coefficient decreases as the velocity 
increases; thus, with a given low velocity, we may trace 
the decrease of the coefficient from 0.0128 for a half-inch 
pipe to 0.0029 for a ninety-six inch pipe; and with a given 
diameter of one-half inch we may trace the decrease of the 
coefficient from 0.0128 for .5 foot velocity per second to 
0.00622 for 14 feet velocity per second, and with a given 
diameter of 96 inches we may trace the decrease of the 
coefficient from 0.0029 for a velocity of .5 foot per second to 
0.00259 for a velocity of 14 feet per second. 

We have then a large range of coefficients applicable to 
clean, smooth, and straight bores. When the bores are of 
coarse grain, or are slightly tuberculated, the range is still 
greater, and the values of coefficients of the smaller diam¬ 
eters quite sensibly affected; and if the bores are very 
rough or tuberculated, the values of coefficient for small 
diameters and low velocities are very much augmented. 

271. Effects of Tubercles.— These effects, in tubercu¬ 
lated pipes, as compared with clean pipes, are illustrated in 
the following approximate table, which we have endeavored 
to adjust to a common velocity of three feet per second for 
all the diameters. The data for very foul pipes is however 
scanty, though sufficient to show that the coefficients do in 


248 


FLOW OF WATER THROUGH PIPES. 


extreme cases exceed the limits given for the small diam¬ 
eters ; and that conditions from clean to foul may occur, 
with the several diameters, that shall cover the entire range 
from minimum to maximum coefficients, and calling for a 
careful exercise of judgment founded upon experience. 


TABLE No. 62. 


Coefficients for Clean, Slightly Tuberculated, and Foul Pipes, 


of Given Diameters, and with a Common Velocity of 3 feet 


per Second. 



Hydraulic 
Mean Radius, 
5 d 

C ~ 4 

Diameter. 

Clean. 

Slightly 

tuberculated. 

Foul. 

.OIO4 

.0156 

Feet . 

.0417 

.0625 

Inches . 

1 

2 

3 

4 

Coe /., m . 

O.OO753 

.OO745 

Coe /., in . 

Coe /., m . 

.0208 

.0834 

I 

.OO734 

O.OO982 


.0312 

• I2 5 ° 


.OO722 

.00940 


.0364 

.1458 

x i 

.00707 

.OO925 


.0417 

.1667 

2 

.00692 

.OO9IO 

O.OI40O 

.0625 

.2500 

3 

.00670 

.00862 

.OI300 

•0833 

•3334 

4 

.00650 

.00825 

.01200 

.1250 

.5000 

6 

.00623 

.OO772 

.OIIOO 

.1667 

.6667 

8 

.00600 

•00733 

.OO922 

.2083 

•8334 

10 

.OO584 

.00706 

.00868 

.2500 

1.0000 

12 

.OO51O 

.00680 

.00828 

• 2 9 x 7 

1.1667 

14 

•00554 

•00657 

.OO792 

•3333 

1-3333 

16 

.OO538 

.00636 

.00760 

• 375 ° 

1.5000 

18 

.00523 

.00616 

.OO733 

.4167 

1.6667 

20 

.OO509 

.00598 

.00710 

.5000 

2.0000 

2 4 

.OO483 

•OO567 

.00664 

• 5 62 5 

2.2500 

2 7 

.OO468 

•OO544 

.00635 

.6250 

2.5000 

3 ° 

.OO452 

• 0 ° 5 2 5 

.00604 

.6875 

2 - 75 °° 

33 

.OO44O 

•OO507 

.00578 

• 75 00 

3.0000 

3 6 

.OO424 

.OO490 

•°°554 

•8333 

3-3333 

40 

.OO407 

.OO466 

.00524 

.9167 

3.6667 

44 

.OO389 

•OO443 

.00500 

1.0000 

4.0000 

48 

.OO376 

.OO422 

.00477 

























EQUATION OF VELOCITY. 


249 


212. Classification of Pipes and their Mean Co¬ 
efficients. —In ordinary calculations, the mean coefficient 
for medium diameters and velocities may be taken, for clean 
pipes, as .00644 ; for rough or slightly tuberculated pipes, 
as .0082 ; and for very rough or very foul pipes, as .012. 
These coefficients apply approximately to pipes of about 
five inches diameter, when the velocities are about three 
feet per second, reference being made to the diameter of the 
pipe itself when clean. 

213. Equation of the Velocity Neutralized by Re¬ 
sistance to Flow. —Having now developed the several 
values of m as applicable to the several conditions of pipes, 
we will again transpose our equation and remove % the 
member expressing velocity of flow, to one side by itself, 
and we have the equation of velocity of flow : 


2, gh"8\ i 
Clm f 

or 

V = i 

(2 qri )I 
| m [ 


2 gdi 1 1 

4 m ( 

or 

H 

;2 ghl'dvk 
| (4 m) l j 


or v 

j 2q7i"r ) i 

~ 1 "ir i 


(8) 


In which h"— the resistance head, in feet. 

I = the length of the pipe, in feet. 
cl — the internal diameter of the pipe, in feet. 

O = the internal circumference of the pipe, in feet. 
S = the sectional area of the pipe, in square feet. 

Ji n 

i the sine of inclination = 


r = the hydraulic mean radius = 


S _ d 
C~ 4 * 







250 


FLOW OF WATER THROUGH PIPES. 


274. Equation of Resistance Head.—By transposi¬ 
tion again we have tlie equation for that portion, lc ] , ot the 
total head H included in tlie slope i : 



Clviv 2 
2gS 


or 


_ ( 4 m) M 
~ 2gd 


or 



tr 

x o“* 



Let c r represent the maximum ratio of ft! to 7i, or coeffi¬ 
cient of resistance of entry of the jet = .5055. 

275. Equation of Total Head.— Then for short pipes, 


or* 


and 


r! 2g 




. I \ V 2 

1 + Cy + fR - ) c r— 

r> 2g 


' 2gR 

v = i . K , l 
1.5 4- m - 


( 10 ) 

( 11 ) 


also, 



The value of c r decreases with v and inversely with 
increase of ft!'. 


276. Equation of Volume.—The velocity v having 
been ascertained, we have, for volume of How q per second, 

v = -zjjtrm and Q = -78^)4:d 2 v ; 

. 7854 ( 1 * 1 


* Compare Weisback’s Mechanics of Engineering, translated by E. B. 
Coxe, A. M. N. Y., 1870, p. 870. 












SUBDIVISIONS OF TOTAL HEAD. 


251 


also, we have 


1 


.7854^ V '' /// x 


1.5 + 4m 

d 


or 


q = .7854V2g x 


Ud° ) 1 


1.5d + 4mZ) 


or 



(13) 


277. Equation of Diameter. —By transposition again 
for the value of d , we have 




(14) 


or 


In this last equation of d , the assistance of the table of 
velocities for given slopes and diameters (p. 259), and the 
table of coefficients, m, for given velocities and diameters 
(§ 269, p. 242), will be required, since the unknown quan¬ 
tities d and m appear in the equation. The approximate 
values of d and m for the given velocity can be taken from 
the tables and inserted in the right-hand side of the equa¬ 
tion, and a close value of d worked out for a first approxi¬ 
mation, and then the operation repeated for a closer value 
of d , if necessary. 

278. Equations of v, h , d 9 and q 9 for long pipes.— 

When pipes exceed one thousand diameters in length the 
following simple formulas may be used, taking values of m 
from table 61, page 242, and value of 2 g = 64.4. 










252 


FLOW OF WATER THROUGH PIPES. 


v = j W' d l 

l 4 ml i 

*= 8.025 -] ^ Cl t J- * 


(14a) 

Amltf 
h = 2 yd 

= .01553 

d 


(14 b) 

§ 

II 

= .01553 Ar ff- 
h 


(14 c) 

q = .7864# j : "f \ *= 6.302 ] 
i 4 ml ' ( 

h"d 5 1 i 
Ami ) 

(lAd) 


in which v, 7i\ and d , are in feet, and q in cubic feet per 
second. For equivalent values of d in inches and in feet, 
see table 104, p. 504. 

279. Many Popular Formulas Incomplete.—The 

fact that the majority of popular formulas for flow of water 
in pipes, as usually quoted in cyclopedias and text-books, 
refer to li + 7i ", or in some cases to 7i' only, and not to H\ 
has led us to treat the subdivisions of H more minutely in 
detail than would otherwise have been necessary. 

Serious errors are liable to result from the application 
of such hydrodynamic formulae by persons not familiar 
with their origin, especially when the problem includes a 
high head of water and short length of pipe. 

280. Formula of M. Chezy. — The formula of 
M. Chezy, proposed a century ago, and into which nearly 
all expressions for the same object, since introduced, can be 
resolved, refers to 7i ' only, or h'+ h'\ and not to H When 

stated in the symbols herein used, it becomes v= < \ \ 

L Vim ) 


* Since the value of v must here be found before h 


(-D 


and K' are 


known, h" has sometimes been assumed for simplicity, to be identical with IT, 


H 


but — may give a very erroneous value of i and consequently of v. 












SUB-HEADS COMPARED. 


253 


As g is introduced in place of 2 g in our equation, m' will 

1 m 
equal — • 

£ 

£81. Various Popular Formulas Compared. —The 

value of treating the question of flow of water in pipes in 
detail may perhaps best be illustrated by computing the 
velocity of flow from our pipe P, Fig. 35, as it is extended 
to different lengths, from 5 feet to 10,000 feet, by a complete 
formula, with m at its legitimate value, and then computing 
the same by several prominent formulas, in the form in 
which they are usually quoted. (See Table No. 63, p. 254.) 

£8£. Sub-lieads Compared. —If we compute the total 
head, to which the velocities, found by the first formula of 
the table, are due, we shall have the sub-lieads, as follows; 
when d = 1 foot. 


H ~ 1 +.505 + 




Lengths in Feet. 

5* 

So- 

IOO. 

1000. 

10,000 

Velocities in Ft. 
per Second. 

63.463. 

51-111- 

43.n1. 

17.386. 

5-392- 

h 

62.542 

40.568 

28.863 

4.694 

• 45 1 

ti 

3 1 - 583 

20.487 

14-575 

2.370 

.228 

h " 

5.878 

38-945 

56.571 

92.941 

99-330 

H 

IOO . O 

100.0 

100.0 

IOO . 0 

100.0 


It is here shown that the values of li and 7i' cannot be 
neglected until the length of the pipe exceeds one thousand 
diameters, under the ordinary conditions of public water 
supplies. 

In our first length of five feet, 7i is about ten and one- 
half times 7i", and 7i' is about five and one-half times 7i". 






































254 


FLOW OF WATER THROUGH PIPES. 


TABLE No, 63. 


Results given by Various Formulas for Flow of Water in 
Smooth Pipes, under Pressure, Compared. 

Data.— To find the velocity, given : Head , H = ioo feet; Diameter , d = i foot; and Lengths , 

/, respectively as follows: 


Authority. 

Equation (12) .. 

Chezy. 

Du Buat . 

Prony (a) . 

“ (0 . 

Eytelwein {a) .. 

“ 0).. 

Saint Vennant.. 
D’Aubuisson (a) 

“ (0 

Neville (a) . 

“ W. 

Blackwell. 

D’Arcy. 

Leslie. 

Jackson . 

Hawksley. 


Equations. 


igH 


v = 


(1.5) + 4 m 


*=]***!* 

( \mlC ) 


v 


88. 5 r- — .03 


(i)*-hyp.log.(i +I .6)* 
v — (9419.75?-/ + .00665)^—.0816. 
v — (9978.7 6 ri + .02375)^ — .15412 


.84 (^—03) 


v = (11703.95 ri + .01698)^ —.1308.241.778 

( dh 

Z ' =5 ° |7 


P 


+ 5 °^ 

11 . 

v = 105.926 (r/) 21 . 

v — (9579?-/ + .00813)^ —.0902 

v = 95.6 Vri . 

Hr 


.= 1 - 

t .c 


.0234?- + .0001085/ 

i 1 

V — 140 { ri )' 1 — 11 ( ri ) 3 .. 

hd ) £ 


P' 


v = 47 - 9*3 




m 


v = 


.00007726 + 

v = 100 ^ri .... 


.00000162 


v — 50 c ( di ) 


„ ( dh ) i 

» = 48.04s | 7VH7 ( 


5 

feet. 


Veloc. 

63.463 

223.607 


216.94 


223.214 


67.40 

246.171 

218.758 

213.761 

62.540 

294.650 

214.267 

244.120 

223.607 

223.607 

62 -555 


Lengths. 


50 

feet. 

IOO 

feet. 

1000 

feet. 

10,000 

feet. 

Veloc. 

Veloc. 

Veloc. 

Veloc • 

51.hi 

43.in 

17.386 

5-392 

7O.7IO 

50.000 

15.810 

5.000 

102.918 

81.510 

13.662 

3 - 978 i 

68.54 

48.446 

15.258 

4.770 

70.480 

49.792 

15.641 

4.842 

76.367 

53.960 

i6 -975 

5-280 

50.00 

40.82 

15-427 

4-985 

73.682 

51-247 

15.232 

4 - 59 2 

69.114 

48.845 

15-384 

4.800 

67.589 

47.804 

15.114 

4.780 

47 080 

38.75° 

14.780 

4.780 

90.263 

63.070 

18.917 

5 - 5°7 

67-715 

47 « 9 I 3 15*140 

4 - 79 1 

77-133 

54.64017.279 

5-464 

70.710 

50.000 

15.810 

5.000 

70.710 

50.000 

15.810 

5.000 

47.084 

38.724 

H -797 

4.804 


In which C = contour of pipe, in feet; 

c = unity for smooth pipes, and 
is reduced for rough pipes. 
d = diam. of pipe, in feet. 

H — entire head, in feet. 
h" — resistance head, in feet. 


/ = length of pipe, in feet. 

m — coefficient of flow. 

r — hyd. mean radius, in feet, = - . 

4 

S = sectional area of pipe, in square feet. 
i = sine of inclination, in feet, = 

/ 

v — velocity of flow, in feet per sec. 













































































PROXY’S ANALYSIS. 


255 


In long pipes, sufficient velocity is converted into pres¬ 
sure to reduce somewhat the contraction of the jet at its 
entrance into the pipe. In very long pipes the effect of this 
contraction becomes insignificant when compared with the 
effect of reaction from the walls of the pipe. 

283. Investigations by Du Buat, Coloumb, and 
Prony. —The investigations of Du Buat and Coloumb led 
them to the conclusion that the velocity of the fluid occa¬ 
sioned a resistance to flow, in addition to that arising from 
the wet perimeter of a channel or pipe, which is propor¬ 
tional to the simple velocity; and afterwards Prony, coin¬ 
ciding with this view, undertook the investigation of the two 
coefficients thus introduced into the formula of resistance to 
flow. 

Since their new coefficient, ft applied to the simple velo¬ 
city and not to the square of the velocity, as does the co¬ 
efficient m, their expression, in our symbols, became 

&-£ = m JV+M; ( 16 ) 

in which 

= h) or K + h".) 

284. Prony’ s Analysis.— Prony analyzed the results 
of fifty-one experiments to determine the values of m and ft 
including eighteen experiments by Du Buat with a tin 
pipe of about one inch diameter and sixty-five feet long; 
twenty-six experiments by Bossut with pipes of about one, 
one and one-quarter, and two-inch diameters, and varying 
in length from thirty-two to one hundred and ninety-two 
feet; and seven experiments by Couplet. Six of these last 
experiments were made with a five and one-quarter inch 
pipe, under a head less than two and one-quarter feet, and 


256 


FLOW OF WATER THROUGH PIPES. 


one with a nineteen-inch pipe with a head of about twelve 
and one-half feet. 

We have quoted above (§ 269) eight of the experiments 
by Du Buat, nine of those by Bossut, and the full seven 
by Couplet, and in the first two included the extremes so 
as to cover their entire range. 

This was a limited foundation upon which to build a 
theory of the flow of water in pipes, nevertheless the attain¬ 
ments of this eminent investigator enabled him to deduce 
from the limited data hypotheses which were valuable con¬ 
tributions to hydrodynamic science. 

From these experiments Prony deduced the values, as 
reduced to English measures, m = .0001061473 ; and j3 = 
.16327. 

285. Eytelwein’s Equation of Resistance to Flow. 

—Eytelwein, investigating the question anew, and believing 
the contraction of the vein at the entrance to the pipe should 
not be overlooked, soon afterward modified the equation to 
the form, 

5 /T7 

H ~ 2go' = • 000085434 ^ + - 2766 v )’ ( 16 ) 

in which c' refers to the effect of the contraction. 

286. D’Aubuisson’s Equation of Resistance to 
Flow. —D’Aubuisson, more than a half-century later, hav¬ 
ing regard more particularly to the experiments of Couplet, 
gave to m and (3 values as follows : 

?; 2 07 

= .000104392 ^ (v 2 + .180449 v). (17) 

287. Weisbacli’s Equation of Resistance to Flow. 

—Weisbach, availing himself of eleven experiments of his 
own with high velocities, and one by M. Gueymard, in ad- 



UNINTELLIGENT USE OF PARTIAL FORMULAS. 257 


dition to the fifty-one above referred to, proposed the fol¬ 
lowing formula as coinciding better with the results of his 
observations: 



1 3\ l V 1 
Viy d 


(.014312 + 


.017155\ l 
Vv J d2g' 


(18) 


This coefficient (a which replaces 4m in our sym¬ 

bols, is founded upon the assumption that the resistance of 
friction increases at the same time with the square and with 
the square root of the cube of the velocity. 


288. Transpositions of an Original Formula.— 

That Chezy’s formula has been generally accepted as one 
founded upon correct principles, we readily infer by its fre¬ 
quent adoption, transposition and modification in the writ¬ 
ings of many philosophers and hydraulicians. Note, for 
instance, the second formulas («) of Eytelwein and D’Au- 
buisson in the above table (No. 63), and the formulas of 
Beardmore, Blackwell, Downing, Hawksley, Jackson, Box, 
Storrow, and others, which may be resolved into this orig¬ 
inal form. 

289. Unintelligent Use of Partial Formulas.— 

That serious errors may arise from an unintelligent and 
improper use of these formulas is conspicuously apparent 
in the above table of results, computed upon conditions in 
the very midst of the range of conditions of ordinary muni¬ 
cipal water supplies. A full knowledge of the origin of a 
formula is essential for its safe practical application. 

A solid body falling freely in a vacuum tlirough a height 
of 100 feet, acquires a rate of motion of only about 80.3 feet 
per second, yet some of the formulas appear to indicate a 
velocity of flow exceeding 200 feet per second, through five 
feet of pipe, under 100 feet head pressure. 


17 



258 


FLOW OF WATER THROUGH PIPES. 


290. A Formula of more General Application.— 

Weisbach has suggested a more comprehensive form of 
expression which includes the head generating the velocity 
of flow and the head equivalent to the dynamic force lost at 
the entry of the jet into the pipe, as well as the head balanc¬ 
ing the resistance to flow in the pipe, and therefore his 
equation presents the equality between the total head //, 
and the sum of the velocity and resistance heads, equal 
to h + 7i'+ 7i". 

Weisbach has also developed a portion of the values 
of m. 

291. Value of v for Given Slopes. —We have here¬ 
tofore insisted that m, as introduced into the equation, shall 
approximate near to its legitimate value for the given condi¬ 
tions. Its value for each given diameter, or hydraulic mean 
radius, r, depends upon the velocity of flow, and therefore 
upon the slope, s , generating the velocity. 

To aid in the selection of m from the tables of m, 
page 242, we have plotted the several velocities as ordinates 
with given sines of slopes, i, as abscissas for such experi¬ 
mental data as was obtainable, and have taken the interme¬ 
diate approximate values of v from their parabolic curves 
thus determined from the experimental data, and have 
arranged the following table of v ; which of course refers to 
the head li\ balancing the resistance in the slope s . 


VELOCITIES FOR GIVEN SLOPES AND DIAMETERS. 259 


TABLE No. 6 4. 


Velocities, 


v , for given Slopes and Diameters. 
For Clean Iron Pipes. 



(i + c r ) -f m 



or 


v — 



Slope. 

Sine of 
Slope. 

Diameters. 

% inch. 
.0417 ft. 

.0625'. 

1" 

.0834'. 

.1250'. 

iV' 

.1458'. 

2 /7 

.l6 67'. 




. h ." 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 




1 

Ft. per sec . 

Ft. per sec. 

Ft. per sec. 

Ft. per sec. 

Ft. per sec. 

Ft. per sec. 

I 

in 

250 

.004 






I.184 

I 

iC 

200 

.005 





1.206 

1.340 

I 

n 

167 

.006 




I.I90 

I.360 

1.500 

I 

n 

143 

.007 




I.29O 

1.453 

1.600 

I 

a 

125 

.008 



I.O38 

I- 39 1 

I.580 

1.730 

I 

il 

nr 

.009 



I.I30 

1.480 

1.700 

I.870 

I 

a 

100 

.OIO 


I.030 

I.24O 

1.600 

I.79O 

I.980 

I 

a 

83-3 

.012 

O.892 

I.140 

I.43O 

1.730 

1-953 

2.219 

I 

a 

71.4 

.014 

O.9IO 

I.230 

I.54O 

1.860 

2.130 

2.360 

I 

ll 

62.5 

.Ol6 

O.99O 

I.340 

I.64O 

2.010 

2.220 

2.5OO 

I 

u 

55*6 

.Ol8 

I.050 

I.450 

I.760 

2.100 

2.350 

2.630 

I 

a 

50.0 

.02 

I.IOO 

I.518 

I.813 

2.276 

2.530 

2.800 

I 

a 

33-3 

.03 

I.44O 

I.920 

2.280 

2.810 

3.100 

3.390 

I 

a 

25.0 

.04 

1.765 

2.298 

2.730 

3-367 

3-694 

4.002 

I 

u 

20.0 

•05 

2.040 

2.600 

3.050 

3-730 

4.280 

5-020 

I 

a 

16.6 

.06 

2.31O 

2.850 

3.400 

4. no 

4.690 

5.500 

I 

a 

14-3 

.07 

2.490 

3.100 

3.640 

4.420 

5.020 

5.9OO 

I 

n 

12.5 

.08 

2.680 

3-300 

3.92° 

4.730 

5-360 

6.3OO 

I 

n 

11.1 

.09 

2.850 

3.540 

4.180 

5-045 

5-630 

6.6lO 

I 

a 

10.0 

.IO 

3.040 

3-730 

4-437 

5.480 

6.009 

6.979 

I 

a 

8-33 

.12 

3-320 

4.180 

4.900 

6.030 

6.650 

7.490 

I 

n 

7.14 

• 14 

3.460 

4.500 

5.290 

6.535 

7.190 

8.010 

I 

a 

6.25 

.16 

3.840 

4.825 

5.640 

7.010 

7.700 

8.500 

I 

a 

5-55 

.18 

4.O9O 

5.108 

5.998 

7.500 

8.221 

8.960 

I 

a 

5.00 

.20 

4.3IO 

5.400 

6.330 

7.880 

8.690 

9.380 

I 

a 

4.00 

.25 

4-830 

6.100 

7.135 

8.770 

9.690 

10.430 

I 

n 

3-33 

.30 

5-359 

6.730 

7.902 

9.650 

10.620 

11.380 

I 

n 

2.50 

.40 

6.260 

7.790 

9.130 

11.225 

12.280 

12.980 

I 

ll 

2.00 

•50 

7.070 

8.818 

io .339 

12.600 



I 

a 

1.66 

.60 

7.800 

9.790 

11.570 




I 

a 

1-43 

.70 

8.470 

10.760 

12.710 



• • • • 

I 

a 

1-25 

.80 

9.140 

11.720 





I 

u 

1.11 

.90 

9.800 

12.600 

• • • • • 

• • • • • 

• • • • • 

• • • • • 

I 

a 

1.00 

I 

10.390 












































































260 


FLOW OF WATER THROUGH PIPES. 


TABLE No. 6 4—(Continued). 

Velocities, v, for given Slopes and Diameters. 
For Clean Iron Pipes. 


Slope. 

Sine of 
Slope. 

Diameters. 

3 inch. 
.250 ft. 

4 " 

- 3333 '- 

6" 

- 5 '- 

8" 

.6667'. 

io" 

-8333'- 

12" 

1.o'. 


. h " 

l — —~ J 

Velocity . 

Velocity . 

Velocity . 

Velocity . 

Volocity . 

Velocity . 


l 

Ft . per sec . 

Ft . per sec . 

Ft . per sec . 

Ft . per sec . 

Ft . per sec . 

Ft . per sec 

i in mi 

.OOO9 

• • • • 

.... 

• . . . 

• • • • 

• • • • 

I.540 

I “ IOOO 

.OOIO 

• • • • 

• • • • 

• • • • 

• • • • 

• • • • 

I.6lO 

i “ 909 

.OOII 

• • • • 

• • • • 

• • • • 

• • • • 

• • • • 

1.680 

1 “ 833 

.0012 

• • • • 

• • • • 

• • • • 


I.6lO 

1.785 

1 “ 769 

.0013 

• • • • 

• • • • 

• • • • 

• • • • 

I.692 

I.880 

1 “ 714 

.OOI4 

• • . • 

• • • • 

• • • • 

• • • • 

I.760 

I.94O 

1 “ 667 

.0015 

• • • • 

• • • • 

• • • • 

• • • • 

I.84O 

2.010 

1 “ 625 

.0016 

• . • • 

. . . • 

.... 

I.640 

I.920 

2.080 

1 “ 588 

.0017 

• • • • 

• • • • 

• • • • 

I.680 

I.99O 

2.148 

1 “ 556 

.0018 

• • • • 

• • • 

• • • • 

1-750 

2-035 

2.200 

1 “ 526 

.OOI9 

• • • • 

• • • • 

• • • • 

1.800 

2.125 

2.270 

1 “ 500 

.0020 

.... 

• • • • 

I- 5 I 5 

1.830 

2.190 

2.325 

1 “ 455 

.0022 

.... 

• • • • 

1.600 

1.930 

2.320 

2-470 

1 “ 417 

.0024 

.... 

• • • • 

I.680 

2.015 

2.430 

2 . 58 o 

1 “ 385 

.0026 

• • • • 

I.415 

I.760 

2.no 

2.525 

2.695 

1 “ 357 

.0028 

. • . . 

I.480 

1.830 

2.220 

2.610 

2.810 

1 “ 333 

.OO30 

I.284 

1-530 

I.920 

2.315 

2.695 

2.925 

1 “ 286 

•0035 

I.4IO 

1.680 

2.100 

2.510 

2.910 

3.140 

1 “ 250 

.OO4 

1-525 

1.790 

2.260 

2.690 

3.085 

3-390 

1 200 

.OO5 

1.710 

2.030 

2.525 

2-993 

3420 

3.845 

1 “ 167 

.006 

I.863 

2.204 

2.790 

3-315 

3-775 

4.215 

1 “ 143 

.OO7 

2.020 

2.460 

3.000 

3.615 

4-075 

4-585 

1 “ 125 

.008 

2.160 

2.670 

3-215 

3-850 

4-370 

4.9 10 

1 in 

.OOg 

2.280 

2.820 

3425 

4.080 

4.610 

5-185 

1 “ 100 

.OIO 

2.425 

2.960 

3.670 

4-285 

4.880 

5480 

1 M 83.3 

.012 

2.675 

3.230 

3-992 

4.710 

5-375 

6.020 

1 “ 71.4 

.OI4 

2.880 

3.480 

4-370 

5105 

5-885 

6.485 

1 “ 62.5 

.016 

3.O7O 

3.710 

4-695 

5490 

6.325 

6.980 

1 “ 55-6 

.018 

3.240 

3 - 9 1 

4 - 9 6 5 

5.825 

6-745 

7435 

1 “ 50.0 

.02 

3498 

4-134 

5.206 

6-175 

7.070 

7.842 

1 “ 33-3 

■03 

4.24O 

5.160 

6430 

7.640 

8.730 

9-715 

1 “ 25.0 

.04 

5.030 

6.no 

7.560 

9.010 

10.200 

11.280 

1 “ 20.0 

•05 

5-674 

6.825 

8.479 

10.062 

12.293 

12.689 

1 “ 16.6 

.06 

6.213 

7-324 

9.828 

11.020 

• • • 


1 “ 14.3 

.07 

6.785 

7-985 

10.062 

12.020 



1 “ 12.5 

.08 

7.250 

8.604 

10.920 

• • • • 

• • • 


1 “ 11.1 

.09 

7-775 

9-!25 

11.583 

• • • • 



1 “ 10.0 

.IO 

8.238 

9703 

12.209 

• • • • 

• • • 


1 “ 8.33 

.12 

9-045 

10.625 

• • • • 

• • • • 



1 “ 7.14 

.14 

9-773 

H- 53 I 

• • • • 

• • 



1 “ 6.25 

.16 

I0 455 

12.383 

• • • • 

• • • • 



1 “ 5-55 

.18 

1 1-075 

• • • • 

• • • • 




1 “ 5 -oo 

.20 

11.883 

• • • • 

• • • • 

• • • • 



1 “ 4.00 

•25 

13.289 

• • • • 


• • • • 

* • • • 


1 “ 3-33 

.30 

• • • • 

• • • • 

.... 

• • • • 

• • • • 

.... 































































VELOCITIES FOR GIVEN SLOPES AND DIAMETERS. 261 


TABLE No. 64 — (Continued). 

Velocities, v, for Given Slopes and Diameters. 
For Clean Iron Pipes. 


Slope. 

Sine of 
Slope. 

Diameters. 

14 inch 
1.1667 ft. 

16" 

I - 3333 / - 

18" 

1.5'. 

30" 

1.6667'. 

24" 

2.0'. 

27" 

2.25'. 



. h " 

Velocity . 

Velocity . 

Velocity . 

Velocity . 

Velocity . 

Velocity . 



1 l 

Ft . per sec . 

Ft . per sec . 

Ft.per sec . 

Ft.per sec . 

Ft . per sec . 

Ft . per sec . 

i in 

2500 

.0004 

• • • • 

• • • • 

• • • • 

• • • • 

• • • • 

.... 

i “ 

2000 

.0005 

• • • • 

• • • • 

• • • • 

• • • • 

• • • • 

2.080 

i “ 

1667 

.0006 

• • • • 

• • • • 

• • • • 

1.655 

I.940 

2.105 

i “ 

1428 

.0007 

• • • • 

1.6lO 

1-755 

I.860 

2.115 

2.285 

i “ 

1250 

.0008 

1.610 

1-738 

1.850 

1-995 

2.265 

2.385 

i “ 

mi 

.0009 

1.710 

1-855 

1-975 

2.I45 

2.405 

2.580 

i “ 

1000 

.OOIO 

I.800 

I.950 

2.070 

2.255 

2.530 

2.700 

i “ 

909 

.OOII 

I.895 

2.065 

2.195 

2.360 

2-655 

2.880 

i “ 

833 

.0012 

1-975 

2.l6o 

2.295 

2-475 

2.785 

3-000 

i “ 

769 

.0013 

2.040 

2-275 

2-395 

2-575 

2.9IO 

3-155 

i “ 

7 i 4 

.OOI4 

2.130 

2-350 

2.500 

2.675 

3 -oi 5 

3.260 

i “ 

667 

.0015 

2.200 

2.425 

2.606 

2.775 

3.120 

3-395 

i “ 

625 

.0016 

2.285 

2.500 

2.685 

2.875 

3-225 

3-515 

i “ 

588 

.0017 

2-375 

2.590 

2-775 

2.970 

3-366 

3.625 

i “ 

556 

.0018 

2.430 

2.640 

2.845 

3.050 

3-430 

3-725 

i “ 

526 

.OOI9 

2.500 

2.725 

2.925 

3.I70 

3-535 

3-825 

i “ 

500 

.0020 

2-550 

2.810 

3.000 

3.230 

3.640 

3-930 

i “ 

455 

.0022 

2.700 

2.950 

3.187 

3-500 

3.835 

4-135 

i “ 

417 

.0024 

2.825 

3-095 

3-320 

3.570 

4.015 

4-335 

i “ 

385 

.0026 

2.950 

3-230 

3-495 

3.730 

4.210 

4-530 

i “ 

357 

.0028 

3.080 

3-355 

3.610 

3-885 

4.388 

4 . 7 I 5 

i “ 

333 

.0030 

3.200 

3-490 

3-755 

4.020 

4-535 

4-905 

i “ 

286 

•OO35 

3-473 

3.800 

4.060 

4.350 

4-935 

5.315 

i “ 

250 

.004 

3-735 

4.060 

4-330 

4.655 

5.290 

5.690 

i 

200 

.005 

4.180 

4-575 

4.901 

5.240 

5-955 

6-373 

i “ 

167 

.006 

4.602 

5-025 

5-400 

5-770 

6.502 

6-975 

i “ 

143 

.007 

5.025 

5-485 

5-844 

6.260 

7.020 

7.520 

i “ 

125 

.OO8 

5-400 

5-845 

6.275 

6.718 

7.515 

8.045 

i “ 

in 

.OO9 

5-725 

6.185 

6.625 

7-125 

7.980 

8-545 

i “ 

100 

.OIO 

6.030 

6.515 

7.000 

7-550 

8.410 

9-025 

i “ 

83-3 

.012 

6-555 

7.124 

7-725 

8.245 

9.240 

10.000 

• i “ 

71.4 

.014 

7.120 

7.785 

8-345 

8.935 

10.025 

10.870 

i “ 

62.5 

• Ol6 

7-655 

8.330 

8.965 

9.640 

10.790 

11 .715 

i “ 

55-6 

.018 

8.170 

8.900 

9.565 

10.295 

II- 5 I 5 

12.085 

i “ 

50 

.02 

8.667 

9.409 

10.104 

10.801 

12.238 

• • • • 

i “ 

33-3 

•03 

10.691 

11.583 

12.369 

13.229 

• • • • 

• • • • 

i “ 

25 

.04 

12.383 

13-445 

• • • • 

• • • • 

• • • • 

• • • • 






























262 


FLOW OF WATER THROUGH PIPES. 


TABLE No. 6 4—(Continued.) 

Velocities, v, for Given Slopes and Diameters. 
For Clean Iron Pipes. 


Slope. 

Sine of 
Slope. 

Diameters. 

30 inch 
2.5 feet. 

33" 

3 - 75 / 

36 /r 

3 *<y 

40" 

3-3333'. 

44 " 

3.6667'. 

48" 

4.0'. 



, h " 

Velocity . 

Velocity . 

Velocity . 

Velocity . 

Velocity . 

Velocity . 



l 

Ft . per sec . 

Ft.per sec . 

Ft.per sec . 

Ft . per sec . 

Ft.per sec . 

Ft . per sec 

i in 

5000 

.0002 

• • • • 

• • • « 

1-457 

I.59O 

I .719 

I.829 

i “ 

3333 

.0003 

I.586 

1.681 

1-797 

I.948 

2.IO4 

2.220 

i “ 

2500 

.0004 

I.83I 

I.962 

2.060 

2.255 

2.420 

2.620 

i “ 

2000 

.0005 

2.085 

2-175 

2.313 

2.530 

2-735 

2.945 

i “ 

1667 

.0006 

2.235 

2.355 

2.550 

2.800 

2.980 

3-200 

i “ 

1428 

.0007 

2.425 

2.550 

2.796 

3.OIO 

3-265 

3-475 

i “ 

1250 

.0008 

2.617 

2-755 

2.950 

3.225 

3-510 

3.725 

i “ 

IIII 

.OOO9 

2.745 

2.960 

3-155 

3-415 

3.695 

3.904 

i “ 

1000 

.OOIO 

2.895 

3.156 

3.320 

3-605 

3.890 

4.150 

i “ 

9°9 

.OOII 

3-065 

3.290 

3.525 

3.810 

4.080 

4-375 

i “ 

833 

.0012 

3.220 

3 . 4 I 5 

3.695 

3-975 

4.260 

4.565 

i “ 

769 

.0013 

3-355 

3.585 

3-848 

4.150 

4.430 

4.780 

i “ 

714 

.OOI4 

3-500 

3.703 

3.995 

4-305 

4.625 

4.936 

i “ 

667 

.0015 

3-655 

3.875 

4.I30 

4.490 

4-795 

5.130 

i “ 

625 

.0016 

3-785 

4.000 

4.285 

4-645 

4.970 

5.295 

i “ 

588 

.0017 

3 - 9 I 5 

4.120 

4-445 

4.800 

5 -II 9 

5-450 

i “ 

556 

.0018 

4.006 

4.245 

4-595 

4-935 

5.255 

5.620 

T “ 

526 

.OOlg 

4.140 

4.400 

4-725 

5-075 

5-400 

5-790 

I “ 

500 

.0020 

4-235 

4-535 

4.880 

5.180 

5-575 

5-924 

I “ 

455 

.0022 

4.445 

4-759 

5 *ii 5 

5 . 5 I 5 

5.845 

6.230 

I “ 

4 i 7 

.0024 

4-650 

5.000 

5.340 

5.785 

6.O95 

6.500 

I “ 

385 

.0026 

4.875 

5-230 

5.575 

6.035 

6-335 

6.780 

I “ 

357 

.0028 

5.065 

5-435 

5.780 

6.307 

6.590 

7.040 

I “ 

333 

.0030 

5.270 

5.660 

5.981 

6-455 

6.850 

7.300 

I “ 

286 

•OO35 

5-695 

6.090 

6.500 

7.000 

7.385 

7.990 

I “ 

250 

.004 

6.080 

6-493 

6.907 

7-495 

7.920 

8.425 

I “ 

200 

.005 

6.835 

7.260 

7-765 

8-375 

8.845 

9-497 

I “ 

167 

.006 

7-495 

7.980 

8.480 

9.205 

9.784 

10.415 

I “ 

143 

.007 

8.080 

8.645 

9.220 

9*935 

IO.585 

11.307 

I “ 

125 

.008 

8.635 

9.245 

9-875 

10.610 

II.360 

12.250 

I “ 

in 

• OOg 

9.215 

9.800 

10.515 

11.230 

12.150 

• • • 

I “ 

100 

.OIO 

9.720 

io .375 

11.100 

11.919 

• • • • 

• • • • 

I “ 

83.3 

.012 

10.780 

11.449 

11.720 

• • • • 

• • • • 

• • • • 

I “ 

71.4 

.014 

n -745 

12.450 

• • • • 

• • • • 

• • • • 

.... 





























VALUES OF h AND h> FOR GIVEN VELOCITIES. 263 


TABLE No. 64 — (Continued). 

Velocities, v, for Given Slopes and Diameters. 
For Clean Iron Pipes. 


Slope. 

Sine of 
Slope. 

Diameters. 

54 inch 

4.5 feet. 

60" 

5 -o'. 

72" 

6.0'. 

84" 

7.06 

96" 

8.0'. 




. _ h" 

Velocity. 

Velocity. 

Velocity. 

Velocity. 

Velocity. 




l 

Ft. per sec. 

Ft. per sec. 

Ft. per sec. 

Ft. per sec. 

Ft. per sec. 

I 

in 

IOOOO 

.OOOI 

I.381 

1.516 

1.661 

I.906 

2.I44 

I 


5000 

.0002 

1-993 

1-945 

2.039 

2.719 

3-033 

I 


3333 

.0003 

2.423 

2.653 

2.919 

3-279 

3-749 

I 


2500 

.OO04 

2.837 

3.OO7 

3-395 

3-779 

4-352 

I 


2000 

.0005 

3 -I 58 

3-441 

3.870 

4.229 

4.880 

I 

<< 

1667 

.0006 

3-490 

3-785 

4.300 

4.600 

5-320 

I 

H 

1428 

.0007 

3-785 

4.100 

4.670 

4.990 

5.780 

I 

a 

1250 

.0008 

4.000 

4-395 

4-950 

5.400 

6.185 

I 

i < 

IIII 

.OOOg 

4-235 

4-685 

5.260 

5.780 

6.600 

I 

IC 

1000 

.OOIO 

4-550 

4-939 

5 - 58 o 

6. no 

6.972 

I 

IC 

9°9 

.OOII 

4.760 

5-215 

5.870 

6.583 

7.285 

I 

u 

833 

.0012 

4-975 

5-465 

6.120 

6.880 

7.600 

I 

Cl 

769 

.OOI3 

5.190 

5.680 

6.340 

7-150 

7 - 9 I 5 

I 

u 

714 

.OOI4 

5.400 

5-935 

6.630 

7-475 

8.250 

I 

<< 

667 

.0015 

5.629 

6.095 

6.859 

7.701 

8.510 

I 

<< 

625 

.0016 

5 - 8 i 5 

6.300 

7.080 

8.000 

8.815 

I 

IC 

588 

.0017 

5-995 

6.500 

7.300 

8.215 

9.100 

I 

u 

556 

.0018 

6.140 

6.685 

7.500 

8.490 

9.360 

I 

u 

526 

.OOI9 

6.300 

6.865 

7.700 

8.725 

9-580 

I 

a 

500 

.0020 

6.528 

7.071 

7-965 

9.049 

9 -S 75 

I 

a 

455 

.0022 

6.840 

7-435 

8-330 

9.480 

10.400 

I 

u 

4 i 7 

.0024 

7-135 

7.770 

8.715 

9.880 

10.890 

I 

u 

385 

.0026 

7-445 

8.080 

9.060 

10.275 

n. 340 

I 

i< 

357 

.0028 

7.740 

8.380 

9-450 

10.611 

11.780 

I 

a 

333 

.0030 

8.060 

8.680 

9.828 

1 1.000 

12.175 

I 

a 

286 

•OO35 

8-735 

9-370 

10.615 

12.550 

• • • • 

I 

u 

250 

.004 

9.300 

10.060 

n -344 

• • • • 

• • • • 

I 

a 

200 

.005 

10.425 

11.304 

12.680 

• • • • 

• • • • 

I 

a 

167 

.006 

11.470 

12.440 

• • • • 

• • • • 

• • • • 

I 

a 

143 

.007 

12.450 

• • • • 

• • • • 

* * * • 

.... 


292 . Values of h and h' for Given Velocities.— 

In Table 65 are given the values of Ji and li for given 
velocities, which are to be subtracted from H to compute 
the height of the slope balancing the resistance R. 

The velocity being known approximately, its correspond¬ 
ing m for any given diameter may be taken from the table 
of page 242, and inserted in the formula: 


























264 


FLOW OF WATER THROUGH PIPES. 


TABLE No. 65. 

Tables of li and h ' due to Given Velocities, h and ti being 

IN FEET AND V IN FEET PER SECOND. 


Velocity. 

I 

h 

h f • 

h + h r 

.80 

.010 

.0050 

.0150 

.98 

.015 

.0075 

.0225 

I -13 

.020 

.0101 

.0301 

I.27 

.025 

.0126 

.0376 

1-39 

.030 

.0151 

.0451 

1.50 

•035 

.0177 

•0527 

I.60 

.040 

.0202 

.0602 

1.70 

.045 

.0227 

.0677 

I.79 

.050 

.0252 

.0752 

1.88 

•055 

.0278 

.0828 

1.97 

.060 

• 0303 

.0903 

2.04 

.065 

.0328 

.0978 

2.12 

.070 

•0353 

.1053 

2.20 

•075 

•0379 

.1129 

2.27 

.080 

.0404 

.1204 

2-34 

.085 

.0429 

.1279 

2.41 

.090 

.0454 

.1354 

2.47 

•095 

.0480 

.1430 

2-54 

.100 

.0505 

.1505 

2.60 

.105 

.0530 

-1580 

2.66 

.110 

• 0555 

.1655 

2.72 

•115 

.0580 

.1730 

2.78 

.120 

.0606 

.1806 

2.84 

.125 

.0631 

.1881 

2.89 

.130 

.0656 

.1956 

2-95 

•135 

.0672 

.2022 

3.00 

.140 

.0707 

.2107 

305 

•145 

.0732 

.2182 

3-11 

.150 

• 0757 

.2257 

316 

•155 

.0772 

.2322 

3.21 

.160 

.0808 

.2408 

3.26 

.165 

.0833 

.2483 

3.31 

.170 

.0858 

.2558 

3.36 

• 175 

.0883 

.2633 

340 

.180 

.0909 

.2709 

345 

.185 

•0934 

.2784 

3.50 

.190 

.0959 

.2859 

3-55 

•195 

.0984 

•2934 

3-59 

.200 

.1010 

.3010 

3-68 

.21 

.1060 

.3160 

3.76 

.22 

.1111 

.33H 

3.85 

.23 

.1161 

.3461 

3-93 

.24 

.1212 

.3612 

4.01 

•25 

.1262 

.3762 

4.09 

.26 

.1313 

.3913 

4.17 

.27 

.1363 

.4063 

4-25 

.28 

.1414 

.4214 

4-32 

.29 

.1464 

.4364 

4-39 

•30 

.1515 

.4515 


Velocity. 

h 

h f 

h + h ' 

4-47 

•3i 

.1565 

.4665 

4-54 

•32 

.1616 

.4816 

4.61 

•33 

.1666 

.4966 

4.68 

•34 

.1717 

•5117 

4-75 

•35 

•1767 

•5267 

4.81 

•36 

.1818 

.5418 

4.87 

•37 

.1868 

.5568 

4.94 

.38 

•1919 

•5719 

5.01 

•39 

.1969 

.5869 

5-07 

.40 

.2020 

.6060 

5-i4 

•4i 

.2070 

.6170 

5.20 

.42 

.2121 

.6321 

5.26 

•43 

.2172 

.6472 

5-32 

•44 

.2222 

.6622 

5.38 

•45 

.2272 

.6772 

5-44 

.46 

• 2323 

.6923 

5-50 

•47 

•2373 

•7073 

5-56 

.48 

.2424 

.7224 

5.62 

•49 

.2474 

•7374 

5.67 

•50 

•2525 

•7525 

5-73 

•5i 

•2575 

•7675 

5-79 

•52 

.2626 

. 7826 

5.85 

•53 

.2676 

•7976 

5-9° 

•54 

.2727 

.8127 

5-95 

•55 

•2777 

.8277 

6.00 

•56 

.2828 

.8428 

6.06 

•57 

.2S78 

.8578 

6.11 

•58 

.2929 

.8729 

6.17 

•59 

•2979 

.8879 

6.22 

.60 

• 3030 

.9030 

6.28 

.61 

.3080 

.9180 

6.32 

.62 

•3131 

•9331 

6-37 

•63 

.3181 

.9481 

6.42 

.64 

.3232 

.9632 

6.47 

•65 

.3282 

.9782 

6.52 

.66 

•3333 

•9933 

6-57 

.67 

•3383 

1.0083 

6.61 

.68 

•3434 

1.0434 

6.66 

.69 

.3484 

1.0384 

6.71 

.70 

•3535 

1-0535 

6.76 

•7i 

•3585 

1.0685 

6.81 

.72 

.3636 

1.0836 

6.86 

•73 

.3686 

1.0986 

6.91 

•74 

•3737 

1.1137 

6-95 

•75 

•3787 

1.1287 

6.99 

.76 

•3838 

1.1438 

7.04 

•77' 

.3888 

1.1588 

7.09 

•78 

•3939 

1-1739 



































TABLES OF h AND h' 


265 


TABLE No. 6 5—(Continued). 

Tables of h and ft due to Given Velocities, h and ft being 

IN FEET AND V IN FEET PER SECOND. 


Velocity. 

h 

h ' 

h + h ' 

7-13 

•79 

•3989 

I.1889 

7.18 

. 80 

.4040 

I.2040 

7.22 

.81 

.4090 

I.2190 

7.26 

.82 

.4141 

1.2341 

7-31 

•83 

.4191 

I.249I 

7-35 

.84 

.4242 

I.2642 

7.40 

-85 

.4292 

I.2792 

7.44 

.86 

•4343 

I.2943 

7.48 

.87 

•4393 

I •3093 

7-53 

.88 

.4444 

1.3244 

7-57 

.89 

•4494 

1-3394 

7.61 

.90 

• 4545 

1-3545 

7.65 

.91 

•4595 

1.3695 

7.70 

.92 

.4646 

1.3846 

7-74 

•93 

.4696 

1.3996 

7.78 

• 94 

•4747 

1.4147 

7.82 

•95 

•4797 

1.4297 

7.86 

.96 

.4848 

1.4448 

7.90 

•97 

.4898 

1.4598 

7-94 

.98 

•4949 

1.4749 

7 . 9 8 

•99 

•4999 

1.4899 

8.03 

1 

.505 

1.505 

8-97 

1.25 

.631 

1.881 

9-83 

1.50 

-757 

2.257 

10.60 

i -75 

.884 

2.634 

11.4 

2 

1.010 

3 " oi o 

n -35 

2.25 

.1.136 

3-386 

12.6 

2.50 

1.362 

3.862 

13-30 

2.75 

1.389 

4-139 

13-9 

3 

I- 5 I 5 

4-515 

14.47 

3.25 

1.641 

4.891 

150 

3-50 

1.767 

5.267 

15-54 

3-75 

1.894 

5-644 

16.05 

4 

2.020 

6.020 

16.54 

4-25 

2.146 

6.396 

17.02 

4-50 

2.272 

6.772 

17.49 

4-75 

2-399 

7-149 

17.94 

5 

2.525 

7.525 

18.39 

5-25 

2.651 

7.901 

18.82 

5-50 

2.777 

8.277 

19.24 

5-75 

2.904 

8.654 

19.66 

6 

3.030 

9-030 

20.06 

6.25 

3.156 

9.406 

20.46 

6.50 

3.282 

9.782 

20.85 

6.75 

3-409 

10.159 

21.23 

7 

3-535 

10-535 

21.61 

7-25 

3.661 

10.911 

21.98 

7-50 

3-787 

11.287 


Velocity. 

h 

h f 

h +/ i ' 

22.34 

7-75 

3 - 9 T 4 

II.664 

22.70 

8 

4.040 

12.040 

23-05 

8.25 

4.166 

12.666 

23.40 

8.50 

4.292 

12.792 

23-74 

8.75 

4.419 

13.169 

24.07 

9 

4-545 

13.545 

24.41 

9.25 

4.671 

13.921 

24-73 

9-50 

4-797 

14.297 

25.06 

9-75 

4.924 

14.674 

25-38 

10 

5.050 

15.050 

25.69 

10.25 

5.176 

15.426 

26.00 

10.50 

5-302 

15.802 

26.32 

10.75 

5-492 

16.242 

26.62 

11 

5-555 

i 6.555 

26.91 

11.25 

5.681 

16.931 

27.21 

11.50 

5.807 

17.307 

27 . 5 I 

11.75 

5-934 

17.684 

27.8 

12 

6.060 

18.060 

28.4 

12.5 

6.186 

18.686 

28.9 

13 

6.565 

I 9-565 

29.5 

13.5 

6.817 

20.317 

30.0 

14 

7.070 

21.070 

30.5 

14.5 

7.322 

21.822 

3 1 • 1 

15 

7-575 

22.575 

31.6 

15.5 

7.827 

23.327 

32.1 

16 

8.080 

24.080 

32.6 

16.5 

8.332 

24.832 

33 -i 

17 

8.585 

25-585 

33-6 

17-5 

8.837 

26.337 

34 -o 

18 

9.090 

27.090 

34-5 

18.5 

9-342 

27.842 

35 -o 

J 9 

9-595 

28.595 

35-4 

19-5 

9.847 

29047 

35-9 

20 

10.100 

30.100 

36.8 

21 

10.352 

31.352 

37-6 

22 

II. IIO 

33-110 

38.5 

23 

11.615 

34 . 6 I 5 

39-3 

24 

12.120 

36.120 

40.1 

25 

12.625 

37 625 

40.9 

26 

13.130 

39 ’ 1 3 ° 

41.7 

27 

I 3.635 

40.635 

42.5 

28 

I4.I4O 

42.140 

43-2 

29 

14.645 

43.645 

43.9 

30 

15.150 

45.150 

47-4 

35 

17.675 

52.675 

50.7 

40 

20.200 

60.200 

53-8 

45 

22.725 

67.725 

56.7 

50 

25.250 

75-250 





































266 


FLOW OF WATER THROUGH PIPES. 


293. Classified Equations for Velocity, Head, 
Volume, and Diameter. —The coefficients ol How lor the 
given slopes and diameters being determined, they, with 
the coefficients of resistance of entry for different forms of 
entrance, may be introduced into the classified equations 
for velocity, and their resolutions for head, volume, and 
diameter completed ; when the equations will become,* 


2 gH 


1 


1.054 +m 

r 

, 1.505+m- 
l r 

2gH 


I for pipes with well-rounded entrances. ($) 


l 

¥ 


for pipes with square-edged flush entrances (5 ) - (19) 


l 


^ 1 for pipes with square-edged entrances pro- / -\ 

1 950 —f - Til — I jecting into the reservoir. ' ' ^ 


fi= 


1 


r 

/l.054 + 

\ rf 2g 

(l.505 + m 
\ r> 2g 

Z\ r> 2 

r) 2g 

fid 5 


(l.956 + m 


<1 = 



1 

¥ 


1.054 d + 4 ml 
lid 5 ' 1 



956d + 4 ml 


d = 


.4788 11.054$ + Ami j- 1 . 
.4788 11.505$ + 4 ml £ i* . 
.4788 11.956$ + Ami . 


(a) 

(b) 

(p) 




( 20 ) 


( a ) 

(b) I- (21) 

(c) 

(«) 

(5) h (22) 

(p) 


* Vide formulas for q and d in § 486 , p. 499 . 

























COEFFICIENTS FOR PIPES. 


267 


294. Coefficients of Entrance of Jet. —Other values 
of c r , for other conditions of pipe entrance, or other coef¬ 
ficients of velocity c v9 may he taken from, or interpolated 
in the following table, computed from the formulas, 



TABLE No. 66. 
Values of c v and c for Tubes. 


° r c .. 

O 

00 

Os 

•974 

•950 

•9 2 5 

.900 

•875 

O 

IT) 

00 

.825 

.815 

.800 

•750 

.715 

.700 

c . 

.041 

•054 

.109 

.169 

•235 

.306 

•383 

.469 

•505 

•563 

•778 

.956 

1.041 

r . 

I + C r .. 

1.041 

1-054 

1.109 

1.169 

1-235 

1.306 

1-383 

1.469 

1-505 

1-563 

1.778 

1.956 

2.041 


295. Mean Coefficients for Smooth, Rough, and 
Foul Pipes. —In ordinary approximate calculations for 
long pipes, it is often convenient to select a mean coefficient 
for medium diameters and velocities, and insert it in a fun¬ 
damental formula as a constant. In such case we may 
select, say, for clean and smooth iron pipes, .00644 ; for 
rough or slightly tuberculated pipes, .0082 ; and for very 
rough or very foul pipes, .012. 

These coefficients are applicable more particularly (wit¬ 
ness table No. 61) to pipes of about five inches diameter 
with a velocity of flow of about three feet per second, and 
to lengths exceeding one thousand diameters. 



we have 





































268 


FLOW OF WATER THROUGH PIPES. 


We may now unite the constant 2 g — 64.4 and our 
assumed constant coefficients, and substitute tlieir algebraic 
equivalents in the equations : 



2 g _ 64.4 
* * 4 m~ 702576 


= 2500. 



2 g _ 64.4 
' * 4m “ .0328 


= 1963.4146. 



2/7 _ 64.4 
* * 4m ~ ."048 


= 1341.6666. 


The equations will in this case become: 


OKAn h d) 1 (7b d ) 1 N 

2500 — 9 — 1 = 50 1 —— r for clean pipes. (a) 


l 


l 


V — < 


Yd . j Yd ) 2 for slightly tuber- 


1963.4146 ^ | 8 = 44.31j~ [' 


cnlated pipes. 


(»> 




1341.6666 — ^ | ~ — 36.63 j — j— i 3 for very foul pipes, (d) 


296. Mean Equations for Smooth, Rough, and 
Foul Pipes. —From these expressions of velocity , in long, 
full pipes, the equations for head, length , and diameter 
may be deduced, thus : 


r 


v = A 


Y = 1 


50 j 

i h d 11 

for clean pipes . • 

(a) 

44.31 | 

\ h"d{ l 

for slightly rough pipes. 

0) 

36.63 < 

\ YdH 
\ l j 

for very rough pipes . 

(«) 

.0004 

Iv 2 
d 

• • • • 

(a) 

.000508 

W 

d 

• • • • 

( 5 ) 

.000745 

Iv 2 
d 

• • • • 

( c ) 





























MEAN COEFFICIENTS. 


269 



r 




2500 

1963.4146 

1341.6666 


dh" 
v 2 
dh" 
v 2 

dh" 



.0004 

.000508 

.000745 


lv 2 

h" ‘ 
lv 2 

W ’ 

lv 2 

h" ' 


(a) 

(») 

(o) 


(25) 


(a) 

(») 

(c) 




(26) 


In which, v = velocity of flow, in feet, per second ; 

h" = head in slope, or mean gradient, in feet; 
l = length of pipe, in feet; 
d — internal diameter of pipe, in feet. 

It is sometimes convenient to express the volume of flow 
per second in a term of quantity, q , rather than in a term of 

velocity. 

Since v— ^ therefore, 


q = Sv — 50 S 


h"d p __ 


39.27 


h"d 5 H 

l 1 


The equations, in terms of qnantity (q), in cubic feet per 
second, will then take the following forms: 



39.27 

Ji"d 5 ' 
( l 

\\ 

* for clean pipes . 

(a) 

<1 = " 

34.80 • 

h"d 5 
l 

\ 

■ for slightly rough pipes 

(») 


28.77 | 

Til'd* \ 

l \ 

\ 

- for very rough pipes . 

(c) 


( 27 ) 






















270 


FLOW OF WATER THROUGH PIPES. 


.0006484 



.000S257 


.001208 


lq 2 
d 5 

l£ 

d? 
lq 2 
d 5 



.00064845 


l = 1 .0008257 


.001208 


7i'd 5 

q 2 

h"d 5 

2 2 




.23034 


m 

Ji" i 

T 

II 

^3 

.24174 


m 

h" 


.2609 

\ lr i\ 

( 7i ") 



(») 

(«) 


(30) 


In which, q = volume of flow, in cubic feet per second ; 

h" = head in slope, or mean gradient, in feet; 
l = length of pipe, in feet; 
d — internal diameter of pipe, in feet. 


297. Modification of a Fundamental Equation 
of Velocity. —The following expressions for velocity, con¬ 
taining the assumed constant coefficient of flow .00644, are 
equivalent to each other: 


v = 




They are sometimes modified by another coefficient, 
thus: 


v = 


j 2 gri) I 
( m ) 


























VALUES OF d. 


271 


to make them conform more nearly to experiment for cer¬ 
tain classes of conditions. 


This coefficient (d) equals unity (d = 1) in cases when 
.00644 is the proper coefficient of flow to embody in the 
fundamental formula 5 is greater than unity {d 1) when 
the principal coefficient should be less than .00644, and 
less than unity (d < 1) when the principal coefficient should 
exceed .00644. Generally, with medium velocities of say 
two and one-half to three feet per second, this coefficient, c\ 
will exceed unity for long clean pipes exceeding five inches 
diameter, and be less than unity for pipes of less than five 
inches diameter. 

298. Values of c'. — When the legitimate coefficient, ?n, 
is replaced by the assumed constant coefficient .00644, then 
approximately, 

.00644 

therefore, 



j 2g -f- m | i _ ( 2 g \ \ 

(2g — .00644) “ ( 10000w ) 


(32) 


With a given velocity of flow of say three feet per second, 
in pipes exceeding one thousand diameters in length, the 
several values of d for different diameters would be approx¬ 
imately as follows : 


TABLE No. 66 a . 
Sub-coefficients of Flow (/) in Pipes. 


Diameter. 

c'. 

Diameter. 

c'. 

Diameter. 

c 

1 

2 

inch. 

• 93 ° 

6 inches. 

I-OIS 

24 

inches. 

I - I 5 ° 

3 

* 

u 

• 93 6 

8 

a 

1.031 

2 7 

<< 

1.170 

I 

U 

.942 

10 

u 

1.050 

30 

U 


I* 

u 

• 95 ° 

12 

u 

1.060 

33 

u 

1.207 


u 

.960 

14 

il 

1.080 

3 6 

u 

1.225 

2 

u 

.970 

16 

u 

i-°95 

40 

u 

i- 2 45 

3 

u 

.980 

18 

a 

I.I IO 

44 

u 

i - 287 .. 

4 

it 

•995 

20 

u 

1.125 

48 

u 

1.308 



























272 


FLOW OF WATER THROUGH PIPES. 


These values of d decrease as the velocity of flow de¬ 
creases from three feet per second, and are approximately 
correct for higher velocities up to ten feet per second. 

BENDS AND BRANCHES. 

299. Bends. —The experiments with bends, angles, and 
contractions in pipes, so far as recorded, have been with 
very small pipes, and the deductions therefrom are of 
uncertain value when applied to the ordinary mains and 
distribution pipes of public water supplies. 

Our pipes should be so proportioned that the velocity 
of flow, at an extreme, need not exceed ten feet per second. 
Our bends should have a radius, at axis, equal at least to 
four diameters. 

Under such conditions, the loss of head at a single bend 
will not exceed about one-tenth the height to which the 
velocity is due (not including height balancing resistance 
of pipe-wall). 

In such case, we may for an approximation take,* 


2 gH 



According to this equation, if a pipe is 1 foot diameter, 
1000 feet long, and flowing with free end under 100 feet 
head, the loss at one 90° bend, whose axial radius of curva¬ 
ture equals 4 diameters, will be .47 feet of head. If there 
are two bends, the total head remaining constant, the loss 


* The mean value of (1 + c r ) for short pipes is 1 . 505 . 









BENDS. 


273 


at botli will not be double this amount, for the velocity 
through the first will be reduced by the resistance in the 


second, and therefore the resistance in the first will be 
reduced proportionally with the square of the reduction of 
the velocity ; and a similar proportional reduction of resist¬ 
ance will take place in the first and second bends when a 
third is added. 

Let v be the velocity due to the given head and length 
of pipe without a bend, and the velocity after the bend is 
inserted, then the height of head lost, fi b , in consequence of 


the bend is 7i h — 


_ (v — Vif 


2g 


and H — 7i b is the effective remain¬ 


ing head. 

After computing the new value of R' beyond the first 
bend, we may substitute that in the equation to find the 
new value of and proceed to deduce the value of H” 
beyond the second bend, etc., or raise the subdivisor to a 
power whose index equals the number of bends ; thus, 


No. of Bends 

I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

Subdivisors. 

•9 

.81 

.656 

• 59 i 

• 53 i 

.478 

•430 

•387 

•349 

• 3 i 4 

.282 

•254 

Reciprocals. 

i .ii 

1.23 

1.52 

1.68 

1.88 

2.og 

2-33 

2.58 

2.87 

3.18 

3-55 

3-94 


For larger pipes, or for larger radius of curvature, or 
reduced velocity, the value of the subdivisor may rise to .94 
or .96, or even near to unity. 

When pipes exceed one thousand diameters in length, 
the term (1 + c r ) may be neglected, and the equations 
assume the following more simple forms, in which the 
reciprocals of the above table, according to the number of 
bends, become the coefficients of m. 


x = 


(2gh 


"ri _) 

1 m f 


(35) 


h" = 


1.111m® 2 


(1.111ml v ' ~ "igri ' 

In which v = the rate of flow, in feet per second ; li 
frictional head; and i = the sine of the inclination. 


a _ 


(36) 

the 



















274 


FLOW OF WATER THROUGH PIPES. 


r — the hydraulic mean radius = 


section 


m 


contour 

a coefficient {vide table of m , page 242), 
64.4. 


The experiments by Du Buat, Venturi, and other of the 
early experimentalists, with pipes varying from one-lialf to 
two inches diameter, and more recent experiments by Weis- 
bach, have been fully and ably discussed by the latter, in 
“Mechanics of Engineering” and elsewhere. 

Weisbach’s formula for additional height of head, 7i by 
necessary to overcome the resistance of one bend, is 

7 <f) V 2 /0 ~v 

7h ~ Z 180 5 * 2g’ ^ 


in which z is a coefficient of resistance, <f> the arc of the bend 
in degrees, and h h the additional head required. 

The value of z he deduces by an empirical formula: 

2 = .131 + 1.847 


in which r is the radius or semi-diameter of the pipe, and R 
the axial radius of curvature of the bend. 

For given ratios of r to R, z has the following values, 
for pipes with circular cross-sections. 


TABLE No. 67 . 
Coefficients of Resistance in Bends. 


r 

R 

.i 


.2 

• 2 5 

•3 

•35 

•4 

•45 

•5 

•55 

z 

•I 3 1 

•133 

.138 

•i 45 

.158 

.178 

.206 

.244 

.294 

• 35 ° 

r 

~R 

.6 

• 6 5 

•7 

•75 

.8 

•85 

•9 

•95 

1 

• • • • 

z 

% 

•440 

. -540 

.661 

.806 

•977 

i-i77 

1.408 

1*674 

i -978 

• • • • 





























































BRANCHES. 


27 5 


300. Branches. —In branches, the sums of the resist¬ 
ances due to the deflections of the moving particles, the 
contractions of sections by centrifugal force, and the con¬ 
tractions near square edges, if there are such, will for each 
given velocity vary inversely as the diameters of the 
branches. 

Until reliable data for other than small pipe branches is 
supplied, we may assume in approximate preliminary 
estimates of head required, when the velocity of flow, under 
pressure, is ten feet per second, a reduction of that portion 

of the head to which the velocity is due (= at a right- 

angled branch, equal to about fifty per cent, in branches of 
three to six inches diameter and thirty to forty per cent, in 
larger branches. 

The equations then take the following form : 


2 gH 



(38) 



(39) 


-The value of the subdivisor will be changed according 
to the special conditions of the given case, and tiie effects 
of a series of branches will be similar to those above 
described for a series of bends, but enhanced in degree. 

For long pipes, equivalent equations will be, 



(40) 


1 . 060 /»®~ 
2 gri 


( 41 ) 











276 


FLOW OF WATER THROUGH PIPES. 


301. Hoav to Economize Head. —Tlie losses of head 
and of energy due to frictions of pipe-wall and to resistances 
of angles, contractions, etc., increase with the square of the 
velocity, and they occasionally consume so much of the 
head that a very small fraction of the entire head only 
remains to generate the final velocity of flow. 

The losses, other than those due to the walls of the pipes, 
originate chiefly about the square edges of the pipes, 
orifices, and valves, where contractions and their resulting 
eddies are produced, or are due to the centrifugal force of 
the particles in angles and bends. 

These losses about the edges may be modified materially, 
even near to zero, by rounding all entrances to the form of 
their vend contractd , and by joining all pipes of lesser 
diameter to the greater by acutely converging or gently 
curved reducers (Fig. 102), so that the solidity and sym¬ 
metrical section of the column of water shall not be dis¬ 
turbed, and so that all changes of velocity shall be gradual 
and icithout agitation among the fluid particles. 

It is of the utmost importance, when head and energy 
are to be economized, that the general onward motion of 
the particles of the jet be maintained, since wherever a 
sudden contraction occurs an eddy is produced, and 
wherever currents of different velocities and directions 
intermingle an agitation results, both of which divert a 
portion of the forward energy of the particles to the right 
and left, and convert it into pressure against the walls of 
the pipe, from whence so much reaction as is across the 
pipe is void of useful effect, and the energy of the jet to a 
like extent neutralized, and so much as is back into the 
approaching column is a twofold consumption of dynamic 
force. 











































WEIR, FOR A TURBINE TEST AT LOWELL, BV JAS. B. FRANCIS, 


















































































































































































































































































































































CHAPTER XIV. 


MEASURING WEIRS, AND WEIR GAUGING. 


302. Gauged Volumes of Flow. —A partially sub¬ 
merged measuring orifice or notch in one of the upright 
sides of a water tank, or a horizontal measuring crest with 
vertical shoulders, in a barrier across a stream, equivalent 
to a notch, is termed a weir. 

Weirs, as well as submerged orifices (§ 206) are used 
for gauging the flow of water, and in their approved forms 
give opportunity to apply the constant force and accelera¬ 
tion of gravity, acting upon the water that falls over the 
weir, to aid in determining the volume of its flow. 

The volume of flow, Q , equals the product of the section 
of the jet upon the weir, S, into its mean velocity, V. 


Q = SV. (1) 

303. Form of Weir. —For convenience in practical 
construction and use, hydraulicians usually form their 
measuring weirs with horizontal crests, CD , and vertical 
ends AC and BD , Fig. 41. 


Fig. 40 . 


Fig. 41 . 



WM% 


1 


,1 


S 


v //////////a 



A 

f 

f 


E 

fl 

tap;;;;, w„IM 

T 

l 




N 

\ 




/ 







A 

—I , 

zzi_j 


z////////7r~ 




























































278 


MEASURING WEIRS, AND WEIR GAUGING. 


The theory of flow over weirs of this description is more 
accurately established by numerous experimental and posi¬ 
tive measurements, than for any other form of notch. 

The head of water upon rectangular w^eirs is measured 
from the crest CD of the weir to the surface of still water, a 
short distance above the weir, instead of from the centre of 
pressure or centre of gravity (§ 206) of the aperture, as in 
the case of submerged orifices. 

The weir is placed at right angles to the stream, with its 
upstream face in a vertical plane. 

The crest and vertical shoulders of the weir are cham¬ 
fered so as to flare outward on the discharge side at an 
angle not less than thirty degrees. The thin crest and 
ends receiving the current must be truly horizontal and 
vertical, and truly at right angles to the upper plane of the 

weir, and sharp-edged, so 
as to give a contracted jet 
analogous to that flowing 
through thin, square-edged 
plate. 

The edges are common¬ 
ly formed of a jointed and 
chamfered casting, or of a 
jointed plate not exceeding 
one-tenth inch thickness, as shown in Fig. 42. 

304. Dimensions. — The dimensions of the notch 
should be ample to carry the entire stream, and yet not so 
long that the depth of water upon a sharp crest shall be less 
than five inches, and if contraction is obtained at the up¬ 
right ends, the section of the jet in the notch should not 
exceed one-fifth the section of the approaching stream, lest 
the stream approach the weir with an acquired velocity that 
will appreciate the natural volume of flow through the notch. 


Fig. 42 . 














END CONTRACTIONS. 


279 


305. Stability. —Care is to be taken to make the foun¬ 
dation of the weir firm, the bracing substantial, and the 
planking rigid, so there shall be no vibration of the frame¬ 
work or crest, and its sheet piling is to go deep, and well 
into the banks on each side, when set in a stream, so that 
there shall be no escape of water under or around it, and a 
firm apron is to be provided to receive the falling water and 
to prevent undermining. 

30G. Varying Length. —Upon mountain streams, it is 
frequently necessary to provide for increasing or shortening 
the length of the weir, so that due proportions of notch to 
volume may be maintained. This may be accomplished by 
the use of vertical stop-planks with flared edges, placed at 
one or both ends of the weir, as at^, Fig. 41. 

Sometimes it is necessary to make the notch of the entire 
width of the stream, when there will be crest contraction 
only, and no end contractions, in which case partitions E 
(Fig. 44) should be placed against the upper side of the 


Fig. 43 . Fig. 44 . 



weir flush with its shoulders and at right angles to its 
plane. On other occasions the weir may be so long as to 
require intermediate posts, F (Fig. 44), in its frame-work, 
when intermediate contractions, one to each side of a post, 
will be obtained, in additions to the crest and end contrac- 
























































































































280 


MEASURING WEIRS, AND WEIR GAUGING. 


tions ; each of which exert an important diminishing influ¬ 
ence upon the volume of flow. 

307. Enel Contractions. —A short weir may be de¬ 
fined, one which is appreciably affected by end contractions 
throughout its entire length; practically, when the length 
of unbroken opening is less than about four times the 
depth of water flowing over. 

The end contractions affect a nearly constant length at 
each end, for each given depth, on long weirs, and such 
length increases with the depth of water upon the weir. 

To obtain perfect end contractions, the distance from 
the vertical shoulder to the side of the channel should 
not be less than double the depth of the water upon the 
weir. 

If there is no end contraction, the volume for any given 
depth is proportional to the entire length of the weir. 

The flow, for a given length, on long weirs, or on w y eirs 
without end contractions, is proportional to a power of the 
depth on the weir. 

308. Crest Contractions^ —To obtain perfect crest 
contractions, the depth of water above the weir should not 
be less than about double the depth upon the weir, especi¬ 
ally when the depth flowing over is less than one foot; and 
the clear fall below the crest to the surface of tail water 
should be sufficient to maintain a perfect circulation of air 
in the crest contraction, d (Fig. 42), under the jet, all along 
the crest. Such supplies of air are to be provided for at 
ends, and at central posts, F (Fig. 44), since a vacuum 
under the jet would defeat the application of the ordinary 
formula. 

309. Theory of Flow over a Weir.— To illustrate 
the deduced theory of flow through rectangular notches, w r e 
will first consider a case independent of contraction: 


THEORY OF FLOW OVER A WEIR, 


281 


Fig. 45 . 



Let a , b , c, d , e,etc. (Fig. 45), be orifices in the side 
of a reservoir, at depths below the water surface, respec¬ 
tively of 1, 2, 3, 4, 5, 6, etc., feet. 

Then the velocity of issue of jet from each orifice will be 

V= V2gH, 


according to its depth, i7, below the surface, viz. : 


For orifice b, V = V2gl 

“ “ c, V = V2g2 

“ “ d,V= V2gS 

“ “ e, V = V2gi 

“ u y = F2f/5 


= 8.03 feet per second. 

= 11.40 “ “ 

= 13.90 “ “ 

= 16.00 “ “ 

= 17.90 “ “ 


u 

u 

(( 

u 

u 


“ i, V = V2ff6 = 19.70 “ 

“ Jc, V = V2g7 = 21.20 “ 

“ n,V = V%8 = 22.70 “ 
“ 0 , V — V2ff9 = 24.10 “ 

“ p, v = V 2(/10 - 25.40 “ 


U 

U 

u 

u 

u 


a 

u 

u 

<< 

u 


Plot each of these depth, a, b, c, etc., to scale upon the 
same vertical line as abscisses and their corresponding 
velocities of issue, bb', cc', dd', etc., horizontally to the same 




























282 


MEASURING WEIRS, AND WEIR GAUGING. 


scale as ordinates; then the extremities of the horizontal 
lines will touch a parabolic line, a, b', d’, p, whose vertex 
is at a, abscissa is ap, ordinates are bb', cc, pp, etc., and 
whose parameter equals 2g. 

Suppose now the lintels separating the orifices are in¬ 
finitely thin, then the volume issuing per second from each 
orifice will equal a prism, whose length and height equals 
that of the orifice, and whose mean projection is equal to 
its ordinate, bb’, cc', dd', etc., or equals in feet, the feet per 
second of velocity of issue from the orifice. 

Again, suppose the partitions to be entirely removed 
and the fluid veins to be infinitely thin and infinite in num¬ 
ber as respects height, then the velocities of the veins plot¬ 
ted to scale, will touch, as before, the parabolic line ab’d'p'', 
and the volume of issue per second will equal a prism whose 
end area equals the notch ap, and whose area of projection 
equals the area of the parabolic segment, app'd’a. 

According to well known properties of the parabola, the 
segment app'd'a is equal to two-thirds its circumscribing 
parallelogram Aapp'. 

Let l be the length of the notch, II the height = ap, and 
V2gH the length of the segment —pp ; then the area of the 
circumscribing parallelogram equals II x V2gH and the 
area of the segment equals II x § V2gII and the volume of 
issue Q = l x H x § V2gH. (2) 

Let V be the velocity of the film of mean velocity. 
Since the volume of the segmental prism app'd'a equals 
two thirds of the parallelopiped Ap of equal height, length, 
and projection, it follows that the volume of the segment 
equals the volume of a parallelopiped of equal height and 
length and of § the projection = pp", and the mean velocity 
of issue, V = pp " = | V2gIL 

The volume Q = l x II x V = l x II x | V2gB. 








FLOW WITHOUT AND WITH CONTRACTIONS. 283 

If tlie crest of the weir is raised to/, then let the height 
af he h , and the velocity of issue of the him at the crest f 
will he V2gh, and the volume of issue q from the notch af 
will he, q = x h x Vh x V2g. 

If the volume q of this segmental prism aff'b'a , he sub¬ 
tracted from the volume Q of the segmental prism app d'a, 
the remainder will equal the volume of the prism fppf — 
Q — q — (f l x H x VII x V2g) — (|l x h x Vh x V2g) = 

ll V2g (HVH-Ji Vh). (3) 

olO. Formulas for Flow without ancl with Con¬ 
tractions. — The formula (2), Q = l x II x f V2g x i ll 
may take the form Q — V2g x l x |UK (4) 

Taking into consideration the complete contraction in a 
rectangular weir, we observe first, that in addition to the 
crest and end contractions, the surface of the stream, Fig. 42, 
begins to lower at a short distance above the weir, and the 
jet assumes a downward curve over the weir. 

Experiments demonstrate that the measurements are 
facilitated, both in accuracy of observations and in ease of 
calculations, by taking the height of water upon the weir 
to the true surface level a short distance above the weir, 
instead of to the actual surface immediately over the crest. 
In such case the top contraction has no separate coefficient 
in the formula of volume. 

Experiments demonstrate also, that a perfect end con¬ 
traction, when depths upon the weir are between three and 
twenty-four inches, and length not less than three times the 
given depth, will reduce the effective length of the weir a 
mean amount, approximately equal to one-tenth of the 
depth from still water surface to crest. 

If II is this depth from surface to crest, and l the full 
length of the weir, and l the effective length of the weir, 
then one end contraction makes l— (l — O.liT); and two 







284 MEASURING WEIRS, AND WEIR GAUGING. 

end contractions make l'= (l — 0 . 2 H ); and any number, 
n, of end contractions make l'= (l — O.lnH). 

The reduction of volume by the crest contraction is com¬ 
pensated for by a coefficient m introduced in the formula 
for theoretical volume, as above deduced. This coefficient 
(m) is to be determined for the several relative depths and 
lengths by experiment. 

If we insert the factors relating to end and crest contrac¬ 
tions, the formula for volume becomes : 

Q = | m x V2g x (l — 0.1 nil)UK ( 5 ) 

The factors f and V2g are constants, and for approximate 
calculations within limits of 3 to 24 inches depths upon the 
weir, m may be taken as constant. 

Let C represent the product of these three factors, then 
C = ^ x V2g. 

The admirable experiments with weirs * upon a great 
scale, which were conducted by James B. Francis, C. E., 
with the aid of the most perfect mechanical appliances, in a 
most thorough and careful manner, give to C a mean value 
of 3.33, and we have 3.33 = § m x V2g. 

Transposing and assigning to V2g its numerical value, 
we have, 

3.33 3.33 

2 x q 02 5 «5 35 — .622 as a mean coefficient. 

^ * 

The formula for volume of flow may take the following 
forms: 

Q=i ^9 x m>{l ~ 0.1 nH)m = B.35m(l - 0.1nff)IJi, (6) 
or for approximate results, 

Q = C{1 — 0.1 nH)Hi - 3.33 (it - 0.1 nH)Hi. {7) 

This last formula, suggested by Mr. Francis, assumes 


* Lowell Hydraulic Experiments; Van Nostrand, New York, 1868. 














INCREASE OF VOLUME DUE TO INITIAL VELOCITY. 285 


that the discharge is from a reservoir infinitely large, so that 
the water approaching has received no initial velocity. 

311. Increase of Volume due to Initial Velocity 
of Water. —When there is appreciable velocity of approach, 
let S be the section of stream in the channel of approach, 
and V the mean velocity of flow in the section S', and h the 
height to which the velocity V is due, and Q the volume 
enhanced by the initial velocity. Then 


S V = Q', and V = and h — 


V 2 

* 9 * 


If the mean velocity, V, is to be determined from the 
surface motion of the water in the channel of approach, let 
V' be the surface motion; then, as will be shown in the 
consideration of flow of water in channels (§ 332), the mean 
velocity is, approximately, eight-tenths of the surface ve- 

(.8 vy 


locity, and V = .8 V ', and li = 


2g 


Fig. 46 . 


Referring again to a parabolic segment of length equal 
to the unit of length of weir, 

Fig. 46, and let H = ap , and 
fi — sa , and V2c)H — pp and 
V2g(lf -y h) = pt. 

The ordinate pp’ of the seg¬ 
ment cipp is the projection of a 
parabolic segment whose volume 
equals the volume of flow when 
the depth upon the weir equals 
ap. 

When the flow has no initial 
velocity the ordinate at a — 0, 

but when the flow has an initial velocity due to the height 
sa = 7i, the ordinate at a equals V2gh = aa\ and the ordi¬ 
nate at p = VWETK) =pt, and any ordinate /, at a 














286 


MEASURING WEIRS, AND WEIR GAUGING. 


depth Ji — sf. , equals V2gh' = ff", therefore the increase 
of volume of flow due to initial velocity is represented by 
the volume aa'tp'f ', and the whole volume of flow by the 
volume apla'. 

This last volume is the volume spt less the volume saa\ 
and equals, for unit of length, 

U (H+ h) V2 f/(jB+h)}-{%h ^/2gh\ = §V2g 

.... ( 8 ) 

Let Q' be the enhanced volume, and let II' be some 
depth, yp, upon the weir, that substituted for H in the 
ordinary formula for Q would give the value of Q'. 

The formula then, if there are no end contractions, is 

Q = \ml V2g H% ( 9 ) 

or, for approximate measures, including end contractions, 
if any, 

Q = 3.33 (7 — 0.1 tiH 1 ) H'K ( 10 ) 

To determine the value of II' from (II + 7i\ substitute 
the value of Q in the equation (8) of volume for one unit of 
length, and we have 

1 V¥g\{H+ h )! - M\ = {%V2g 11% 

and reducing, we liave 

H' = (11) 

i 

If the volume of flow (Q — \ml V2y IP) is known, and it 
is desired to find the depth H upon a weir of given length, 
then by transposition we have, 

yy— f_ Q _ ? f . 

(|ml V2g) 


( 12 ) 







COEFFICIENTS FOR WEIR FORMULAS. 


287 


or, in case of initial velocity in the approaching water, 


H= 


Q 

\ml a/2 g 


+ TC* 




The first of these two values of H will give results suf¬ 
ficiently near for all ordinary practice, if the initial velocity 
does not exceed one-half foot per second. 

In the above formulas of volume the symbols represent 
values as follows: 

Q — volume due to natural flow, in cubic feet per second. 
I = length of weir, in feet. 

I — effective length of weir, in feet. 

m = coefficient of crest contraction, determined by exper¬ 
iment. 

H — observed depth of water upon the weir, in feet. 

8 = section of channel leading to the weir, in square feet. 
V = mean velocity of water approaching the weir, in feet 
per second. 

h — head to which this velocity is due, in feet. 

2 g = 64.3896, or 64.4 for ordinary calculations. 

H =r head upon the weir, when corrected to include effect 
of initial velocity of approaching water. 

Q = volume of flow, including effect due to initial velocity 
of approaching water. 


312. Coefficients for Weir Formulas. — The con¬ 
trolling influence of the contractions entitle them to a 
detailed study. 

In Mr. Francis’ formula for volume, quoted above, the 
end contraction is assumed to be a function of the depth, 
and the crest contraction to be compensated for by the 
coefficient C, of which m is the variable factor dependent 
upon the depth. 



288 


MEASURING WEIRS, AND WEIR GAUGING. 


In tlie following table the quantities in columns A, B , 
D, E , F have been selected from Mr. Francis’ table, the 
column C reduced from its corresponding column, and the 
column G computed. Each of the columns are means of a 
number of nearly parallel experiments, and .they are here 
arranged according to depth upon the weir. 


TABLE No. 68. 

Experimental Weir Coefficients. 


A. 

B. 

c. 

D. 

E. 

F. 

G. 

Length of weir = /, 
in feet. 

Corrected depth 
upon weir — //', 
in feet. 

Quantity of water 
passing weir, in 
cu. ft. per sec. 

= Q'. 

Quantity computed 
by 

^2 g(l — o.mH') 
in cu. ft. per sec. 

Quantity computed 
by 

3.33 (/ — o.inH') H'"- 
in cu. ft. per sec. 

I 

<*- ly 

c V 

<D ~ 

t—1 e» « 

e 3 

> 11 

0 

Value of m. 

9-997 

.62 

16.2148 

16.0382 

16.0502 

3.3275 

.622 

9-997 

• 6 5 

17.3401 

17.1990 

17.2 187 

3.3262 

.622 

9-995 

.80 

23-79 0 5 

23.882 I 

23.8156 

3-3393 

.624 

9-997 

.80 

23-43 0 4 

23.4OH 

23-439 1 

3-3246 

.621 

9-997 

• 8 3 

25.0410 

2 4 ' 8 3 i 3 

24.7548 

3.3403 

.624 

9-995 

.98 

32.5 6 30 

32.3956 

32.2899 

3-3409 

.624 

9-995 

I.OO 

33-4946 

33.2534 

33 . 2 S 33 

3-327o 

.622 

9-997 

I.OO 

32.5754 

32.5486 

32.6240 

3-3223 

.62 I 

9-997 

I.06 

36.0017 

35.8026 

35-5602 

3.3527 

.627 

9-997 

I.25 

45-5654 

45 - 4 I 25 

45.3608 

3-3338 

.623 

9-997 

!- 5 6 

62.6019 

62.6147 

62.8392 

3 - 3 i8 i 

.620 

7-997 

.68 

14.5478 

14.4581 

14.4247 

3-3368 

.624 

7-997 

1.02 

26.2756 

26.2686 

26.0333 

3.3601 

Mean, 

.628 

.623 


Mr. Francis points out the necessity of caution in apply¬ 
ing the above formula for Q beyond the limit covered by 
the experiments, but it occasionally becomes necessary to 
use some formula for depths both less and greater than is 
included in the above table. 

After plotting with care the results obtained in various 
































DISCHARGES FOR GIVEN DEPTHS. 


289 


experiments by different experimentalists, we suggest tlie 
following coefficients tor tlie respective given depths, until a 
series ol equal range shall be established by experiments 
with a standard weir gauge. At the same time, we advise 
that weirs be so proportioned that the depths upon them 
shall conform to the limits already covered by experiment, 
or at least between 4 and 24 inches depths, and with length 
equal to four times the depth. 


TABLE No. 69. 

Coefficients for Given Depths upon Weirs (in thin vertical 

plate). 


Depths. -j 


1 in. 
.083 ft. 

1 i in. 

.124 ft. 

2 in. 
.167 ft. 

3 in. 
.25 ft. 

4 in. 
•333 ft- 

6 in. 
.500 ft. 

8 in. 
.667 ft. 

10 in. 

•833 L 

Value of m . 


.6100 

.6120 

3 . 274 . 

.6140 

3-285 

.6170 

.6195 

3 .314. 

.6223 

■ 3 . 32 Q 

.6235 

3-336 

.6240 

3 338 

Value of C . 


3- 26 3 







Depths.| 

12 in. 
i ft. 

14 in. 
1.167 ft. 

16 in. 
z -333 ft- 

18 in. 
1.500 ft. 

20 in. 
1.667 ft- 

24 in. 
2.000 ft. 

30 in 
2.500 ft. 

40 in. 

3-333 ft- 

48 in. 
4.000 ft. 

Value of in . 

.6241 

.6242 

.6243 

.6242 

.6241 

.6240 

.6232 

.6226 

.6200 

Value of C . 

3-339 

3-339 

3 - 34 ° 

3-339 

3-339 

3-338 

3-334 

3 - 33 1 

3 - 3 z 7 


313. Discharges for Given Depths. —The following 
table of approximate flow over each foot in length of a 
sharp-crested rectangular weir has been prepared to aid in 
adjusting the proportions of weirs for given streams. End 
contractions are not here allowed for.* The coefficients C 
(in ClIU) are taken from table above, and l equals unity. 

The proportions of weir and its ratio to section of chan¬ 
nel are here supposed to conform to the general suggestions 
given above. 

* To compensate for a single end contraction, in long weirs, deduct from 
the total length, in feet, an amount equal to one-tenth the head upon the weir, 
in feet. Reduce the total length a like amount for each end contraction. 

19 





























































290 


MEASURING WEIRS, AND WEIR GAUGING. 


TABLE No. 70. 


Discharges, for Given Depths over each Lineal Foot of Weir. 


Head from 
still water 
in ft ,— H . 

3 

H\ 

Cu. ft. per 
second for 

1 ft. length 

= CIH \ 

Head. 

3 

H *. 

Cubic feet. 

Head. 

3 

H *. 

Cubic feet. 

.04 

.0080 

.0261 

.46 

.3120 

1.0386 

1.2 

I. 3 N 5 

4.3904 

•05 

.0112 

.0365 

.48 

.3326 

i.1072 

1-3 

I.4822 

4.9506 

.06 

.OI47 

.0480 

•50 

•3536 

I-I 77 I 

1.4 

I.6565 

5.5327 

.07 

.OI85 

.0604 

•52 

•3750 

1.2483 

1-5 

I.8371 

6.1341 

.oS 

.0226 

.0738 

•54 

.3968 

1.3209 

1.6 

2.0239 

6.7576 

.09 

.0270 

.0881 

•56 

.4191 

1 • 395 1 

i -7 

2.2165 

7-3987 

.10 

.0316 

.1032 

•53 

.4417 

1.4724 

1.8 

2.4150 

8.0611 

.11 

.0365 

.1195 

.60 

.4648 

1-5475 1 

1.9 

2 6190 

8.7421 

.12 

.0416 

.1361 

.62 

.4882 

1.6286 

2.0 

2.8284 

9.4413 

•13 

.0469 

•1536 

.64 

.5120 

1.7080 

2.1 

3.0432 

10.1581 

.14 

.0524 

.1718 

.66 

•5362 

1.7888 

2.2 

3.2631 

10.8924 

•15 

.0581 

. 1906 

.68 

.5607 

1.8705 

2-3 

3.4881 

11.6289 

.16 

.0640 

.2102 

.70 

•5857 

1.9540 

2.4 

3.7181 

12.3960 

• 17 

.0701 

.2303 

•72 

.6109 

2.0380 

2-5 

3.9528 

13.1788 

.18 

.0764 

.2510 

•74 

.6366 

2.1237 

2.6 

4.I924 

13.9773 

.19 

.0328 

.2721 

.76 

.6626 

2.2104 

2.7 

4.4366 

I 4 . 79 I 5 

.20 

.0894 

.2938 

•78 

.6889 

2.2996 

2.8 

4-6853 

15.6208 

.22 

. 1032 

•3407 

.80 

.7155 

2.3883 

2.9 

4.9385 

16.8486 

.24 

.II76 

.3882 

.82 

.7426 

2.4788 

3 -o 

5.1962 

17.3239 

.26 

.1326 

•4377 

.84 

.7699 

2.5699 

3 -i 

5.4581 

18.1809 

.28 

.1482 

.4892 

.86 

•7975 

2.6620 

3-2 

5.7243 

19.0676 

•30 

•1643 

• 5445 

.83 

.8255 

2-7557 

3.3 

5•9948 

19.9687 

•32 

• I 79 ° 

•5999 

.90 

•8538 

2.8500 

3-4 

6.2693 

20.8830 

•34 

.1983 

.6572 

.92 

.8824 

2-9455 

3-5 

6-5479 

21.8110 

.36 

.2160 

•7158 

• 94 

.9114 

3.0432 

3-6 

6.8305 

22.7525 

•33 

.2342 

.7761 

.96 

.9406 

3-I407 

3-7 

7.1171 

23.7071 

.40 

.2530 

.8384 

.98 

.9702 

3-2395 

3.8 

7.4076 

24.571a 

.42 

.2722 

.9020 

1.00 

1.0000 

3-3390 

3-9 

7.7019 

25-5472 

. 44 

.2919 

.9672 

1.1 

1 - 1 537 

3-8522 

4.0 

8.0000 

26.5360 


-• •• .1 

The coefficients derived from the experiments of Castel 
and D’Aubuisson, Du Buat, Poncelet and Lebros, Smeaton 
and Brindley, and Simpson and Blackwell, have been 
deduced by those eminent experimentalists to compensate 
for all contractions. In such cases, the ratio of length of 
weir to depth, especially where depth exceeds one-fourth 
the length, and the ratio of length to breadth of channel by 
which water approaches, exert controlling influences upon 
the coefficient. 













































WEIR COEFFICIENTS. 


291 


The following table of coefficients, deduced by Castel, 
show the influence of depth and length. 

In these experiments, Castel used for channel a wooden 
trough 2 feet 5| inches wide, and the weir placed upon its 
discharging end was in each case of thin copper plate. 


TABLE No. 71. 

Weir Coefficients, by Castel. 


o 

*5 '*“* C/3 

cl a v 

Canal, 2.427 feet wide. 

t 

Coefficients, the lengths of the overfall being respectively 

Qi 

Q c.° 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

3 

2.42 

2.23 

1.96 

1.64 

1 -3 1 

0.98 

0.65 

0.32 

0.16 

O.O9 

0.06 

0.03 

Ft. 

0.78 








o-595 

0.615 


0.639 


.72 


. 




.... 

. 

•594 

.614 


•639 


•65 


. 




. 

0.596 

•594 

.614 

0.629 

.640 

0.670 

•59 






. 

•595 

•594 

.613 

.628 

. 641 

.672 

•52 


. 




. 

•595 

•592 

• 613 

.628 

.642 

.674 

•45 


.... 




0.603 

•593 

•592 

.612 

.628 

■643 

• 675 

•39 


• • « • • 



0.621 

.604 

•592 

.591 

.612 

.628 

• 645 

.678 

•32 


0.657 

0.644 

0.631 

.621 

.604 

•593 

•59i 

.612 

.627 

.648 

.687 

.26 

0.662 

.656 

.644 

.632 

.620 

.606 

•595 

•592 

.612 

.627 

• 652 

.698 

.19 

.662 

.656 

■ 645 

.632 

.622 

.610 

.604 

•595 

.612 

.628 

.658 

.713 

. 16 

.662 

.656 

.644 

• 6 33 

.626 

.616 

.6ll 

•597 

• 613 

.629 

• 663 

.... 

.13 

. 662 

.656 

■ 645 

.636 

.632 

.623 

.619 

.604 

.614 

«... 

669 

.... 

.09 

.663 

.660 

.651 

.642 

.636 

.631 

.624 

.618 

.... 

.... 

.... 

.... 


If we plot certain series of experiments by Smeaton and 
Brindley, Poncelet and Lesbro, Du Buat, and Simpson and 
Blackwell, and take the corresponding series of coefficients 
from the resulting curves, we have the following results for 
the given depths and lengths. 


TABLE No. 72. 

Series of Weir Coefficients. 



^5 <u 

° , 4 > 

Cfi t — 



Depths upon Weir, 

in Feet. 




Experimenters. 

Lengtl 
weir, ir 

Ft. 

Ft. 

Ft. 

Ft. 

A*. 

A*. 

Ft. 

Ft. 

Ft. 

A’/. 

Ft. 

Ft. 


0.075 

0.1 

0 15 

0.2 

0.25 

o -3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

Smeaton and Brindley. 

0.5 

.682 

.667 

.640 

.623 

.613 

.605 

•596 

•593 

•485 

.482 

.480 

.478 

Poncelet and Lesbros. 

.646 

.625 

.618 

.608 

.600 

•597 

•593 

•590 

.488 

Du Buat. 

1-533 

•673 

.662 

•645 

•635 

.629 

.624 

.622 

.628 

•635 

.560 

•. 


Simpson and Blackwell.... 

u u u 

3 -° 

.740 

•725 

.700 

.678 

•657 

.638 

.608 

•592 

•577 

• . 

• .. 

IO.O 

.615 

•638 

•673 

. 7OO 

.718 

•735 

•754 

.767 

.780 

•793 


• • 









































































































292 


MEASURING WEIRS, AND WEIR GAUGING. 


Within the limits of depths covered by the above experi¬ 
ments the coefficients all increase as the depths decrease, 
except in the last series belonging to the 10 foot weir. The 
curves in each instance begin to bend rapidly at depths of 
about tliree-tentlis feet. In the two last series above, the 
convexities of the curves are opposed to each other, and the 
curves cross at a depth of .275 feet. 

314. Vacuum under the Crest. —If the partitions E 
(Fig. 44) are prolonged below the weir so as to close the 
ends of the crest contraction, and the fall is slight to surface 
of tail water, the moving current will withdraw sufficient 
air from under the fall to produce a vacuum in the crest 
contraction, from which will result an increased flow over 
the weir. Such vacuum will take place if the surface of 
the tail water rises to the level of the crest when there is 
two and one-half or more inches depth flowing over the weir. 

The tail water may rise near to the crest of the weir, if 
no vacuum is produced, without materially affecting the 
volume of flow. 

315. Examples of Initial Velocity. —Mr. Francis 
found that with a half foot depth upon the weir, a half foot 
per second initial velocity of approach increased the dis¬ 
charge about one per cent., and with one foot upon the 
weir, one foot per second initial velocity increased the dis^ 
charge about two per cent. 

When initial velocity exists in the approaching water, 
and the flow is irregular, with eddies, results of submerged 
obstructions or irregular channel, the channel should be 
corrected, and, if necessary, a grating placed in the stream 
some distance above the weir, so that the water will ap¬ 
proach with steady and even flow upon each side of the 
channel’s axis, so that correct measurements may be taken 
of the height of the surface of the stream above the weir. 


WIDE-CRESTED WEIRS. 


293 


31G. Wide-Crested Weirs. —If the crest of the weir is 
thickened, as in the case of an unchamfered plank, the jet 
tends to cross in contact with its full crest breadth, and the 
contraction is distorted. This is especially the case when 
the depth upon the weir is less than three inches. 

If the edge receiving the current is not a perfect angle 
not greater than a right-angle, that is, if it is worn or 
rounded, the jet tends to follow the crest surface and dis¬ 
tort the contraction. 

In such cases the ordinary formula are not applicable, 
and the safest remedy is to correct the weir. 

When the weir crest is about three feet wide, and level, 
with a rising incline to its receiving edge, as in Fig. 47, Mr. 
Francis suggests a formula for approximate measurements, 
when end contractions are suppressed, for depths between 
six and eighteen inches, as follows: 

Q — 3.0120 81 B 1 ’ 53 (12) 

The coefficient m is here .563 approximately. 


Fig. 47. 



In Mr. Blackwell’s experiments on weirs three feet wide, 
both level and inclined downward from the receiving edge 
to the discharge, coefficients m were obtained, as follows, 
applicable to the formula 

Q = | ml V2gBK 


(13) 



294 


MEASURING WEIRS, AND WEIR GAUGING 


TABLE No. 73. 

Coefficients for Weir Crests Three Feet Wide. 


Depths from 
still water 
upon the 
the weir. 

3 feet long, 
level. 

3 feet long, 
inclined. 

1 in 18. 

3 feet long, 
inclined. 

1 in 12. 

6 feet long, 
level. 

10 feet long, 
level. 

10 feet long, 
inclined. 

1 in 18. 

Feet . 

VI . 

m . 

VI . 

m . 

VI. 

VI . 

.083 

•452 

.545 

•467 

• • • # 

.381 

.467 

.167 

.482 

.546 

•533 

• • • • 

•479 

•495 

.250 

.441 

• 537 

•539 

.492 

.... 

• • • • 

•333 

.419 

•431 

•455 

•497 

• • • • 

•515 

.417 

•479 

.516 

• • • • 

.... 

.518 

• • • 

.500 

.501 

• • • • 

• 53 i 

•507 

• 5 i 3 

•543 

•533 

.488 

• 513 

•527 

•497 

• • • • 

... 

.667 

.470 

.491 

• • • • 

• • • • 

.468 

•507 

• 750 

.476 

.492 

.498 

.480 

.486 

• • • • 

.833 

• • • • 

• • • • 

• • • • 

• 465 

•455 

• • • • 

•9*7 

• • • • 

• • • • 

• • • • 

.467 

• • • • 

• • • • 

1.000 

• • • • 

• • • • 

• • • • 

• • • • 

• • • . 

• • • • 


317. Triangular Notches.— Prof. James Thomson, of 
the University of Glasgow, proposed, in a paper read before 
the British Association at Leeds, in 1858, a triangular form 
of measuring weir. In his experiments with such weir, the 
depths of water varied from 2 to 4 inches, and the volumes 
from .033 to .6 cubic feet per second. From his experi¬ 
ments he derived the formula (with h in inches) 

Q = 0.317 7il (14) 

The flow for all depths would be through similar tri¬ 
angles, therefore an empirical formula applies with greater 
reliability to varying depths. 

Prof. Thomson claimed that “in the proposed system 
the quantity flowing comes to be a function of only one 
variable—namely, the measured head of water—while in 
the rectangular notches it is a function of at least two vari¬ 
ables, namely, the head of water, and the horizontal width 
























OBSTACLES to accurate measures. 


295 


of the notch; and is commonly also a function of a third 
variable, namely, the depth from the crest of the notch 
down to the bottom of the channel of approach.” 

When the stream is of such magnitude as to require a 
considerable number of triangular notches (say of 90° 
angles, or isosceles right-angled triangles) for a single gauge, 
the greatest nicety will be required to place the inverted 
apices all in the same exact level, so one measurement of 
depth only may suffice for all the notches. 

The angles of the notches in each weir must conform 
exactly to the angles of the notch from which the empirical 
formula, or series of coefficients for given depths, was de¬ 
duced. 

For large volumes of water, the great length required 
for a sufficient number of notches, as well as depth required 
in each notch, are often obstacles not easily overcome, and 
the mechanical refinement necessary to ensure accuracy of 
measurement is often difficult of attainment. 

318. Obstacles to Accurate Measures.—A correct 
measurement of the depth of water upon a weir is not so 
easily obtained as might be supposed by those unpractised 
in hydraulic experiments. 

If the weir is truly level and the shoulders truly vertical, 
which are results only of good workmanship, and the 
length intended to be some given number of even feet, the 
chances are that only a skilled workman will have brought 
the length within one, two, or even three-thousandths of a 
foot of the desired length. Again, when the weir is truly 
adjusted and its length accurately ascertained, it is not 
easy to measure the depth upon the crest within one or two 
thousandths of a foot, without excellent mechanical devices 
for the purpose. 

The errors due to agitation or ripple upon the water and 


296 


MEASURING WEIRS, AND WEIR GAUGING. 


the capillary attraction of tlie measuring-rod have to be 
eliminated. 

If tlie graduated measuring-rod is of clean wood, glass, 
steel, copper, or any metal for which water has an affin¬ 
ity, and its surface is moist, or is wetted by ripple, tlie 
water will, in consequence of capillarity, rise upon it above 
the true water level; or if, on the other hand, the rod is 
greasy, the water may, in consequence of molecular repul¬ 
sion, not rise upon it to the true surface level. 

These sources of error may not be of much consequence 
in gaugings of mountain streams, when the only object is 
to ascertain approximately the flow from a given watershed; 
but in measurements of power, and in tests of motors, tur¬ 
bines, and pumps, they are of consequence. 

Upon a weir ten feet long, with one foot depth of water 
flowing over, an error of one-tliousandth of a foot in meas¬ 
urement of depth will affect the computation of flow about 
0.30 cubic feet per minute, and an error of one-thousandth 
of a foot (about ^ of an inch) in length will affect the com¬ 
putation about two-tenths of a cubic foot per minute. 

These amounts of water upon a twenty-five or thirty foot 
fall would have quite appreciable effects and value. 

319. Hook Gauge.—A very ingenious and valuable 
instrument for accurately ascertaining the true level of the 
water surface, and depth upon a weir to still water, was 
invented by Uriah Boy den, C. E., of Boston, and used by 
him in hydraulic experiments as early as tlie year 1840. 

This, shown in one of its forms, in Fig. 48, is commonly 
termed a hook gauge. 

This gauge renders capillary attraction a useful aid to 
detect error, instead of being a troublesome source of error. 

The instrument is firmly secured to solid substantial 
beams or a masonry abutment, so that it will be suspended 


HOOK GAUGE. 


297 


over tlie water channel a few feet up¬ 
stream from the weir, and where the 
water surface is protected, naturally 
or artificially, from the influence of 
wind and eddies. The gauge is here 
adjusted at such a height that when it 
reads zero the point of the hook shall 
accurately conform to the level of the 
crest of the weir; or the vernier reading 
is to be taken, with the hook at the 
exact weir level, for a correction of 
future readings. 

This correction is to be verified as 
occasion requires between successive ex¬ 
periments. 

When the full flow of water over the 
weir has become uniform, the hook is 
to be carefully raised by the screw mo¬ 
tion, until the point just reaches the 
surface of the water. If the point is 
lifted at all above the water surface, the 
water is lifted with it by capillary at¬ 
traction, and the reflection of light from 
the water surface is distorted and reveals 
the fact The screw is then to be re¬ 
versed and the point slightly lowered 
to the true surface. 

In ordinary lights, differences of 
0.001 of a foot in level of the water are 

easily detected by aid of the hook, 
® and even 0.0001 of a foot by an expe- 


1 — rienced observer in a favorable light. 
Such gauges are ordinarily gradu- 

































































































































298 


MEASURING WEIRS, AND WEIR GAUGES. 


ated to hundredths of a foot and are provided with a ver¬ 
nier indicating thousandths of a foot, and fractions of this 
last measure may be estimated with reliability. 

320. Rule Gauge. — For rougher and approximate 
measures a post is set at an accessible point on one side of 
the channel, above the weir, and its top cut off level at the 
exact level of the weir crest. 

The depth of the water is measured by a rule placed 
vertically on the top of this post and observed with care. 

321. Tube and Scale Gauge.— For summer meas¬ 
ures, a pipe, say three-fourth inch lead, is passed from the 
dead water a little above the weir, through or around the 
weir, and connected to a vertical glass water tube set below 
the weir at a convenient point of observation. In such case 
a scale with fine graduations is fastened against the glass 
with its zero level with the weir. With such an arrange¬ 
ment quite accurate observations can be taken, as the 
water in a three-quarter inch tube will rise to the level of 
the water above the weir over the open mouth of the tube, 
due precautions being taken to keep sediment out of the 
tube. 

321a. Weir Volumes. —Table No. 70, page 290, has 
been computed with a variable C , as in table 69, as is proper 
for close accuracy. Table 73a gives results more in detail, 
but is computed with a constant coefficient, by formula No. 7, 
page 284, for each hundredth of foot-depth, from 0.2 ft. to 
3.0 ft. The intermediate thousandths of a foot-depth may 
readily be interpolated. 


WEIR VOLUMES. 


298a 


TABLE No. 73a. 

Computed Weir Volumes. 

On sharp crest, Q = 3.33 (L — 0.1 n H) (§ 310, p. 284), for each lineal 

foot of weir. 

(See also foot note page 289, for effect of contractions.) 


Depth, 
in feet. 

.OO 

.OI 

.02 

-°3 

.04 

•05 

.06 

.07 

.08 

.09 



Discharge Q, in cubic feet per second. 

Length 

d 

H 

II 

n = 0 . 


.2 

0.2978 

0.3205 

0.3436 

0-3673 

o-39 x 5 

0.4162 

0.4415 

0.4672 

0.4934 

0.5200 

•3 

0.5472 

o.574 8 

0.6028 

0.6313 

0.6602 

0.6895 

0.7193 

0-7495 

0.7800 

o.8no 

•4 

0.8424 

0.8742 

0.9064 

0.9390 

0.9719 

1.0052 

1.0389 

1.0730 

1.1074 

1.1422 

•5 

1-U73 

1.2128 

1.2487 

1.2849 

1-3214 

1-3583 

1-3955 

1-4330 

1.4709 

1.5091 

.6 

I-547 6 

1.5865 

1.6257 

1.6652 

1.7050 

1-7451 

1-7855 

1.8262 

1.8673 

1.9086 

•7 

1.9503 

1.9922 

2.0344 

2.O77O 

2.1198 

2.1629 

2.2063 

2.2500 

2.2940 

2.3382 

.8 

2.3828 

2.4276 

2.4727 

2.5180 

2.5637 

2 6096 

2.6558 

2.7022 

2.7490 

2-7959 

•9 

2.8432 

2.8907 

2.9385 

2.9865 

3.0348 

3-0831 

3.1322 

3-1813 

3.2306 

3.2802 

1.0 

3-3300 

3.3801 

3-4304 

3.4810 

3.53i8 

3.5828 

5.6342 

3-6857 

3.7375 

3-7895 

1.1 

3- 8 4 i8 

3-8943 

3-9470 

4.OOOO 

4.0532 

4.1C67 

4.1604 

4-2143 

4.2684 

4.3228 

1.2 

4-3774 

4.4322 

4-4873 

4.5426 

4.5981 

4.6538 

4.7098 

4.7660 

4.8224 

4.8790 

i-3 

4-93S 8 

4.9929 

5.0502 

5 1077 

5-1654 

5-2233 

5.2814 

5.3398 

5-3984 

5-4572 

1.4 

5.5162 

5-5754 

5-6348 

5.6944 

5-7542 

5-8143 

5.8745 

5-9350 

5.9957 

6.0565 

i-5 

6.1176 

6.1789 

6.2404 

6.3020 

6.3639 

6.4260 

6.4883 

6.5508 

6.6135 

6.6764 

1.6 

6-7394 

6.8027 

6.8662 

6.9299 

6-9937 

7-0578 

7.1221 

7.1865 

7.2512 

7-3 i6 o 

i-7 

7-3 8i o 

7-4463 

7-5 ri 7 

7-5773 

7-643 1 

7.7091 

7.7752 

7.8416 

7.9081 

7-9749 

i.8 

8.04x8 

8.1089 

8.1762 

8.2437 

8.3113 

8.3792 

8.4472 

8.5154 

8.5838 

8.6524 

1.9 

8.7212 

8.7901 

8.8592 

8.9285 

8.9980 

9.0677 

9-1375 

9.2075 

9.2777 

9 348 i 

2.0 

9.4187 

9.4894 

9.5603 

9.6314 

9.7026 

9-7741 

9-8457 

9-9174 

9.9894 

10.062 

2.1 

10.134 

10.206 

10.279 

10.352 

10.425 

10.498 

10.571 

10.645 

10.718 

10.792 

2.2 

10.866 

IO.94O 

n.015 

11.089 

11.164 

11.239 

11.314 

11.389 

n.464 

11.540 

2-3 

11.615 

11.691. 

H 

H 

O' 

ix.843 

11.920 

11.996 

12.073 

12.150 

12.227 

12.304 

2.4 

12.381 

12.459 

12.536 

12.614 

12.692 

12.770 

12.848 

12.927 

13.005 

13.084 

2-5 

13-163 

13.242 

13.3 2 i 

13.401 

13.480 

13.560 

13.640 

13.720 

13.800 

13.880 

2.6 

13.961 

14.041 

14.122 

14.203 

14.284 

14-365 

14.447 

14 528 

14.610 

14.692 

2.7 

14-774 

14.856 

14.938 

15.021 

16.103 

15.186 

15.269 

I5.352 

15.435 

I 5 . 5 I 9 

2.8 

15.602 

15.686 

15-769 

15.853 

15-938 

16.022 

16.106 

16.191 

16.275 

16.360 

2.9 
* 3-° 

16.445 

17-305 

16.530 

16.616 

16.701 

16.787 

16.872 

16.958 

17.044 

a 

17.130 

17.217 


If there is velocity of approach (§ 811, p. 285) divide the 
weir volume as above by section of channel, in square feet, 
for approximate velocity v. Then the additional depth on 
weir due to this velocity is h — (V 64.4). Add to the 
measured depth 1.5 li for the corrected depth on weir, and 
then take the volume from the above table for the corrected 
depth, or for closer accuracy compute by formula No. 10, 
page 286, with coefficient from table 69. 

The coefficient of h (1.5) becomes 2.05 approximately 
when there is velocity of approach with end contraction. 




























Fig. 



tucrtorr* 


_ 



Fig. 3 . 



4 



MODERN CURRENT METERS 

















































CHAPTER XT. 

FLOW OF WATER IN OPEN CHANNELS. 


322. Gravity the Origin of Flow.— Gravity tends to 
cause motion in all bodies of water. Its effects upon tlie 
flow of water under pressure liave been already discussed 
(Chap. XIII), as have also the effects of the reactions and 
cohesive attractions that retard its flow. 

The same influences control the flow of water in open 
channels. 

The fluid particles are attracted toward the earth’s 
centre along that path where the least resistance is op¬ 
posed. 

An inclination of water surface of one-thousandth of a 
foot in one foot distance leaves many thousand molecules 
of water, but partially supported upon the lower side, and 
they fall freely in that direction, and by virtue of their 
weight press forward the advanced particles in lower planes. 


Fig. 49 . 



If water is admitted from the reservoir A, into the open 
canal B (Fig. 49), until it rises to the level bb\ it will there 
stand at rest, although the bottom of the channel is in¬ 
clined, for its surface will be in a horizontal plane. The 

















300 


FLOW OF WATER IN OPEN CHANNELS. 


resistances to motion upon opposite inclosing sides, and 
also upon opposite ends, balance eacli otlier. The alge¬ 
braic sum of horizontal reactions from the vertical end bd , 
is exactly equal to the sum of the horizontal reactions from 
the inclined bottom db\ for the vertical projection, or trace 
of the inclined area, db exactly equals the vertical area bd. 

The same equilibrium would have resulted if the bot¬ 
tom had been horizontal or inclined downward from d to 
and a vertical weir placed at fb\ for the horizontal reaction 
from fb' would have been balanced by the sum of the hori¬ 
zontal reactions from bd and df. 

A destruction of equilibrium permits gravity to generate 
motion. 

If a constant volume of water is permitted to flow from 
the reservoir A into the channel 7i, the water surface will 
rise above the level bb\ when there will be less resistance at 
the end b' than at b , and the fluid particles, impelled by the 
force of gravity, will flow toward b'. When motion of the 
water is fully established, and the flow past b' has become 
uniform, there will result an inclination of the surface from 
a toward a'. This inclination, being a resultant of a con¬ 
stant force, gravity may be used as a measure of the por¬ 
tion of that force that is consumed in maintaining the * 
velocity of flow. 

323. Resistances to Flow. —Let the channel be ex¬ 
tended from V (Fig. 49) indefinitely, and with uniform in¬ 
clination, as from cl to b (Fig. 50). Some resistance to flow 
will be presented by the roughness and attraction of the 
sides and bottom of the channel. 

If the sides and bottom are of uniform quality, as re¬ 
spects smoothness or roughness, the amount of their resist¬ 
ance in each unit of length will be proportional to the sum 
of their areas, plus the water surface in contact with the 


EQUATIONS OF RESISTANCE AND VELOCITY. 


301 


air reduced by an experimental fractional coefficient; and 
to the square of the velocity of flow past them; and in¬ 
versely to the section of the stream flowing past them. 

The exact resistance due to the air perimeter, has yet to 
be separated and classified by a series of careful experi¬ 
ments, but we may assume that the resistance of calm air 
for each unit of free surface will not exceed ten per cent, of 
that for like units of the bottom and sides of smooth chan¬ 
nels, and will bear a less ratio for rough channels. 

The air perimeter resistance will be increased by oppos¬ 
ing and lessened by following winds. 

Let R be the sum of resistances from the sides, bottom, 
and surface, in foot pounds per second ; C, the contour, or 
wetted area of sides and bottom, and c s the width, or sur¬ 
face perimeter, in square feet; S, the sectional area of the 
stream, in square feet; and v, the mean velocity of flow of 
the stream, in feet per second; then we have for equation 
of resistance to flow, from sides, bottom, and surface, for 
one unit of length : 


R = 


C + M 
S 




and for any length, l, in lineal feet, 


^ C -f .1 c 3 7 mv 1 
R = —— f x l x 


S 


2g 



324. Equations of Resistance and Velocity.— 

When the surface of the water is level the entire force of 
gravity acts through it as pressure, but when the surface is 
inclined, a portion of the pressure is converted into motion . 
Motion is measured by its rate or distance passed through 
in the given unit of time, and the rate is expressed by the 
term velocity. 





302 


FLOW OF WATER IN OPEN CHANNELS. 


In Fig. 50, let a'7c be the inclination of the water surface 
in a unit of length of the stream, then a" 7c will be its ver¬ 
tical distance and Tc’Tc its horizontal distance. 

The effective action of gravity g to maintain motion, or 
velocity of the water, is dependent on this slope, and the 
slope is usually indicated by a ratio of the vertical distance 
to the horizontal distance. 


Fig. 50 . 



Let h" be the vertical distance a" 7c and Z be the hori¬ 
zontal distance Tc'Tc , and i the slope, or sine of the inclina- 

Ji" 

tion, then the ratio of slope is i = -j-. 


If the sides and bottom of the channel opposed no resist¬ 
ance to How, then the velocity v should be accelerated in 
the length 7c'1c an amount equal to the V2gh", but the how 
being uniform, the sum of the resistances in Z just balance 
the accelerating force of gravity g, and the velocity v con¬ 
tinues from a' to 7c at the same rate that had already been 
established when the stream reached a which was due to 


some height aa' — 7i — 


v < 


2g- 


By transposition, we have v = V2g7i. 

If the sum of the resistances in the length 7c'7c balance 
the accelerating force due to the head a"7c = h ", then we 
have 



C + .1 c s 

x —g— x Im. 

s hr i_ 

C + .1 c s x Z x m 



v 2 = 2g x 


( 4 ) 
























EQUATIONS OF RESISTANCE AND VELOCITY. 


303 


The inverted fractional term 


S 


Section 


is 


0 + .1 c s ~ Contour* * 
termed in open channels the hydraulic mean depth, and 
the letter r is used to express it. Since i expresses the 

h" 

value of the sine of the slope — we have 

L 


( m ) 


<»j 


h" = 


Imv 2 


2gr * 


( 6 ) 

The total head H equals the heights aa' + a"7c = h + h", 


and 


IT 


h + h"=H=-^ + 


Imv 2 


2g 2 gr 


1 + 


Im 
r ! 


x 


v 


(7) 


v = 


2gH 


1 + m 


l 





In long canals and rivers, with slopes not exceeding 
three feet per mile, the velocity head h is usually insig¬ 
nificant compared with the frictional head h", and may be 
neglected in the equation. 

When the rate of flow is uniform, h is a constant quan¬ 
tity, independent of the length, and when the mean velocity 
is known may be taken, by inspection, from the table of 
“ Heads ( h ) due to given Velocities,” page 264. 

The frictional head h" increases with the length, hence 
the term l in the equation of h". 


s 

* In full pipes — equals the sectional area divided by the full circumfer- 

G 


ence, and is termed the hydraulic mean radius (§ 208 ), but in open channels 
the contour is the wetted perimeter; that is, the sum of the sides and bottom 
and air surface in contact with the water. 














304 FLOW OF WATER IN OPEN CHANNELS. 

The mean velocity, which multiplied into the sectional 
area of the stream will give the volume of discharge, is a 
quantity often sought. 

Neglecting the value of h — —, which has given the 

*9 

stream its resultant motion, and taking the formula for h ", 
the head balancing the resistance to flow, 

7 ■ „ _ lmv~ 

2gr ’ 

and we have by transposition, 


v = 




in which v = mean velocity of all the films, in feet per sec. 

S 

r = hydraulic mean depth = — in feet. 

L -j - O.J-C s 

h" 

i = sine of inclination = -j in feet. 

g — 32.2. 

m = a comprehensive variable coetflcient. 

C = wetted earth perimeter. 

c s = surface (air) perimeter, taken at 0.1c, for 
smooth channels, or 0.05c, for rough channels. 

I = length, referred to a horizontal plane. 
h' r = vertical fall in the given length. 

325. Equation of Inclination. —If the flow is to be 
at some predetermined rate, and it is desired to find the 
inclination, or slope to which the given velocity, for the 
given hydraulic mean radius, is due, then we have, by 
transposing again, 

. mv % 

^ = o—* 

2 gr 


( 10 ) 







COEFFICIENTS OF FLOW IN CHANNELS. 


305 


The member v, refers to the mean motion of all the fluid 
threads, or the rate which, multiplied into the section of the 
stream, gives the volume of flow. 

326. Coefficients of Flow for Channels. —The value 
of the coefficient of flow m, is very variable under the influ¬ 
ences of 

(a.) Velocity of flow, or inclination of water surface ; 

(b.) Hydraulic mean depth ; 

(c.) Mean depth; 

(d.) Smoothness or roughness of the solid perimeter; 

(e.) Direction and force of wind upon the water surface. 

A complete theoretical formula for flow in a straight, 
smooth, symmetrical channel should have an independent 
coefficient for each of these influences, and other coefficients 
for influences of bends, convergence or divergence of banks, 
and eddy influences; but such mathematical refinement 
belongs oftener to the recitation room than to expert field 
practice. 

The comprehensive coefficient m, for open channels, 
which includes all these minor modifiers, is inconstant in a 
degree even greater than the coefficient m for full pipes, 
which we have already discussed (§ 270. Peculiarities of 
the Coefficient of Flow), to which the reader is here referred. 

Experience teaches that m is less for large or deep, than 
for small or shallow streams; for high velocities, than for 
low velocities ; and for smooth, than for rough channels. 

Kutter adopted, 5 "' for open channels, the simple formula 
y = c Vri , and divided the values of c into twelve classes, 
to meet the varying conditions, from small to great velocities 
and sections of streams, and from smooth to rough sides 


* Vide “ Hydraulic Tables,” trans. by L. D. A. Jackson. London, 1876 . 



306 


FLOW OF WATER IN OPEN CHANNELS. 


and beds of channels. His c corresponds to y ^, as herein 

7 /A 


employed, and a portion of its values are : 


r. 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

X. 

XI. 

XII. 

.5 

85-5 

82.5 

77-9 

72.4 

66.9 

61.1 

55-8 

49-5 

43 - 2 

36.7 

29.7 

22.5 

.6 

85.6 

83.8 

79-5 

74.2 

68.9 

63.3 

58.x 

51-8 

45-5 • 

38-9 

3 X, 7 

24.1 

• 7 

87-5 

84.8 

80.7 

75-6 

70-5 

65.1 

59-9 

53-8 

47-4 

40.7 

33-4 

25-5 

.8 

88.2 

85.6 

81.7 

76.8 

7 x -9 

66.5 

61.5 

55-4 

49.0 

42-3 

34-9 

26.8 

•9 

88.8 

86.4 

82.6 

77-9 

73 -o 

67.8 

62.9 

56.9 

50-5 

43-8 

36.2 

28.0 

I 

89-3 

87.0 

83-3 

78.7 

74.0 

69.0 

64.1 

58.2 

57-8 

45 -o 

37-5 

29.1 

2 



• • • • 

• • • • 

.... 

• • • • 

.... 

.... 

60.3 

53-7 

45-9 

36-7 

*3 




. . . . 

• . • • 

.... 

• • • • 

• . . 

65.0 

58.7 

5°-9 

4 I -S 

4 



• • • • 

.... 

.... 

.... 

• • . • 

• • • • 

68.3 

62.1 

54-5 

45 -° 

5 


.... 

.... 

• • • • 

• • • • 

.... 

• • • • 

.... 

70.6 

64.8 

57-3 

47.8 

6 



.... 

• • • • 

... 

• • • • 

• . • • 

... 

72.5 

66.8 

59-5 

50.1 

7 



• • • • 

• • • • 

.... 

• • • 

.... 

.... 

74.0 

68.s 

61.3 

52.0 

8 


• • • • 

.... 

• • • • 

• • • • 

.... 

.... 

.... 

75-2 

69.9 

62.9 

53-7 

9 

... 

... 

• • • • 

. • • • 

.... 

.... 

.... 

• • • • 

76-3 

71.1 

64.2 

55 -i 

00 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 

IOO 


327 . Observed Data of Flow in Channels.—Let us 

deduce the several values of m from various actual meas¬ 
urements of streams, and seek its curve of mean values, so 
that when it is a divisor of the simple fundamental equation 
v = V2gri, we shall have some degree of confidence in the 
use of this simple equation for channels and small streams. 
For this purpose we will select at random from data given 
by Messrs. Humphreys and Abbott, 1861; M.M. Darcy 
and Bazin, 1865; M. Heinr Gerbenau, 1867; and sundry 
reports of U. S. Engineer Corps, and compute the experi¬ 
mental value of m for each case.* 

It will be observed that the data cover ranges as follows : 
Of sectional area , from 9.5 to 15911 sq. feet; of hydraulic 
mean depth , from .96 to 15.9 feet; and of velocity, from 
.817 to 4.689 feet per second, or from three-quarters to about 
three and one-quarter miles per hour. 


* The same, with additional data for large rivers, has been used by General 
H. L. Abbott, in a paper upon Gauging of Rivers, for the purpose of testing 
the new (Humphreys and Abbott) formula for flow of rivers, vide Jour. PranK, 
lin Institute, May, 1873 , 
































































TABLE OF COEFFICIENTS FOB CHANNELS 


307 


Observed 


TABLE No. 74. 

and Computed Flows in Canals and Rivers. 



Name of Stream. 

A. 

B. 

C. 

D. 

E. 

F. 

G. 

Area = S. 

Wetted 
Perimeter 
= C. 

Hy. mean 
Depth — r. 

Inclination 
— i. 

Observed 

V elocity 

= V. 

Value of 

Coefficient 

= m. 

Computed 

Velocity 

= V. 

• 

Sq.ft. 

Feet. 

Feet. 

Feet. 

Feet. 


Feet. 

Feeder Chazilly. 

9-5 

9.9 

0.96 

0.000792 

1-234 

.03215 

*•*33 


n -3 

10.8 

1.04 

.000445 

0.962 

.03227 

0.966 

it it 

M -9 

12.3 

1.21 

.000808 

1.667 

.02265 

1-547 

it it 

18.1 

131 

1.38 

.000450 

1.296 

.02381 

1.275 

it it 

18.8 

13-3 

1.41 

.000993 

1.798 

.02789 

1.926 

it it 

19.4 

13.8 

1.41 

.000858 

1.815 

.02363 

1.794 

it it 

22.2 

14.4 

i -54 

.000986 

1.959 

.02548 

2.062 

it it 

22.9 

HZ 

1.56 

.000842 

1.998 

.02118 

1.930 

it it 

27.2 

i 5-9 

I - 7 I 

.000441 

1.510 

.02130 

1.496 

Feeder Grobois. 

IO. I 

10.2 

0.98 

.000555 

0.984 

.03617 

1.063 

it it 

11.8 

“•3 

1.05 

.000310 

0.817 

•03155 

0.852 

it it 

17.2 

12.5 

i -38 

.000450 

1.326 

.02274 

1.278 

it it 

23.° 

14.1 

1.63 

.000479 

1-434 

.02445 

1.502 

ii it 

259 

14.x 

*• 7 * 

.000515 

1.746 

.01860 

1.617 

it it 

26.8 

15-7 

1.71 

.000493 

1.683 

.01917 

1.585 

it it 

3 °. 8 

u -3 

1.78 

.000275 

1.467 

.01465 

1.231 

ii it 

32.0 

17-3 

1.85 

.000330 

I. 4 II 

.01974 

1.381 

Speyerbach . 

30.2 

19.7 

i -54 

.000467 

1.814 

.01408 

1.422 

Canal. 

50.0 

20.6 

2.40 

.000063 

1 .134 

•00757 

0.743 

Lauter Canal. 

56.4 

31.0 

1.82 

.000664 

2.106 

.01754 

I *934 

Saalach. 

86.9 

61.2 

1.38 

.001036 

2.155 

.01982 

*•934 

it 

96.7 

71.8 

i -34 

.001136 

1.970 

.02585 

1.980 

it 

119.0 

3 2 -S 

3 - 7 ° 

.000698 

2.723 

.02243 

3-523 

C. and O. C. Feeder. 

121.0 

32.7 

3 - 7 ° 

.000699 

3. 0 32 

.01811 

3-527 

River Haine. 

248.5 

50.5 

4.90 

.000165 

2.495 

.00836 

2.146 

Isaa. 

3 o°.i 

161.6 

1.85 

.002500 

3-997 

.01864 

3.812 

ii 

3 ° 6.4 

53-4 

5 - 7 ° 

.000155 

2.558 

.00869 

2.328 

Seine. 

1978 

349 

5 - 7 ° 

.000127 

2.094 

.01063 

2.107 

B. La Fourche. 

2868 

230 

15.7 

.000044 

2.789 

.00572 

3.110 

ii 

3025 

232 

13.0 

.000037 

2.843 

.00383 

2.311 

it 

3738 

238 

15.7 

.000045 

3.076 

.00481 

3-145 

Seine. 

442 r 

4°5 

10.90 

.000140 

3-741 

.00702 

3-8io 

ii 

6372 

439 

14.50 

.000140 

4.232 

.00730 

5.062 

ii 

8034 

5°4 

15.90 

.000172 

4.682 

.00803 

6.326 

ii 

9522 

5*8 

18.40 

.000103 

4.689 

.00268 

5 - 99 1 

Rhine. 

I 4 i 5 ° 

1458 

9.72 

.000112 

2.910 

.00828 

3-037 

Upper Mississippi. 

I 59 11 

1612 

9.87 

.000074 

2.941 

.00544 

2 - 55 + 


328. Table of Coefficients for Channels. — From 
the experimental results we deduce the following values of 
m for the given hydraulic mean depths. Since 2 g is a con¬ 


stant, we have also the corresponding values 




































































308 


FLOW OF WATER IN OPEN CHANNELS. 


TABLE No. 75. 


Values of m for Open Channels, and Values of 
for Given Hydraulic Mean Depths. 



5 


^iG 

II 

m . 

i/S- 

• 

«0|<J 

II 

m . 

/ 2 g _ 

j m ' 

• 2 5 

.0500 

35 • s 9 

7 

.OO96 

81.90 

•3 

.0478 

36.70 

7-5 

.OO92 

83.66 

-4 

.0440 

38-25 

8 

.0088 

85-54 

•5 

.0408 

39-73 

8-5 

.0085 

87.04 

.6 

.0378 

41.27 

9 

.0081 

89. l6 

•7 

•°353 

42.71 

9-5 

.OO77 

91-45 

.8 

•° 33 2 

44.04 

10 

.0074 

93.28 

•9 

.0312 

45-43 

11 

.0068 

97 - 3 i 

1.0 

.0298 

46.49 

12 

.0064 

100.30 

1.25 

.0260 

49-77 

13 

.0058 

105-36 

i -5 

.0234 

52.46 

14 

.0054 

109.21 

2 

.0197 

57-17 

i 5 

.0049 

114.65 

2 -5 

.0172 

61.19 

16 

.OO43 

122.37 

3 

• OI 53 

64.87 

17 

.OO4O 

126.88 

3-5 

.0137 

68.56 

18 

.0036 

133-77 

4 

.0127 

71.21 

19 

•OO33 

139.69 

4-5 

.0118 

73-87 

20 

.OO30 

146-53 

5 

.0112 

75-83 

21 

.OO29 

149.04 

5-5 

.0107 

77-58 

22 

.OO27 

1 * 54-44 

6 

.0102 

79.46 

23 

.0025 

160.49 

6-5 

.0099 

80.65 

25 

.0020 

179.44 


These values of m and of 

> 



— were inserted in the 
m 


simple formula, v 



and were used for a 


test to compute the velocities in the column G , of the above 
table of experimental data. The computed velocities may 
there be compared with the observed velocities. The results 
are satisfactory, if the exceeding difficulty of securing an 
accurate measurement of mean velocity of the stream and 
the probability of small errors are considered. 

























VARIOUS FORMULAS OF FLOW COMPARED. 309 

Tlie velocities in the experimental table above, cover the 
range in ordinary practice, excepting the extremes of floods 
and droughts. The values of m are for the mean range of 
velocities there given. A considerable increase of velocity 
would reduce, or of roughness of channel would increase, 
the value of m for its given hydraulic mean depth. The 
influences of bends and eddies are to be eliminated from the 
formula, since the formula applies to a straight, smooth, 
symmetrical channel. 

Jackson gives,* from Darcy, Bazin, Gauguillet, and 
Kutter, variable coefficients for the channel surfaces named, 
as follows. (These appear to be applicable to a constant 
value of v , equal to about 2.5.): 

.018, Well-planed plank. 

.020, Glazed pipes, or smooth cement lining. 

.022, Smooth cement and sand mortar lining. 

.024, Unplaned plank. 

.026, Brickwork and cut-stone lining. 

.034, Rubble masonry lining. 

.040, Canals, in very firm gravel. 

.050, Rivers in earth, free from stones and weeds. 

.070, “ with stones and weeds in great quantities. 

329. Various Formulas of Flow Compared. —To 
compare this simple formula, having its variable m , with 
some of the more complex formulas, in the forms in which 
they are generally quoted in text-books and cyclopedias, 
four experiments are taken from the table, having their 
hydraulic mean depths and sectional areas of mean, mini¬ 
mum, and maximum values, and their velocities are com¬ 
puted by it. The velocities are then computed by well- 
known formulas upon the same data. The results are given 
in the following table : 


* Hydraulic Manual. London, 1875 . 




310 


FLOW OF WATER IN OPEN CHANNELS. 


TAB LE No. 76. 


Formulas for Flow of Water in Channels, to find the Velocity. 


Comparing results given by the several formulas. 


Authority. 


Eq- (9), § 324 • 
Du Buat. 

Eytelwein ... 

Girard. 

Prony. 

D’Aubuisson. 

Neville. 

Leslie. 

Pole. 

Beardmore... 

Darcy and ) 
Bazin. J 

M. Hagen_ 

Humphreys ) 
and Abbott. j 


Formulas. 


v=\ U. 

( m ) 


88.51 (r* * * § — .03) 0 , £ N 

- f - -— — .o84(r 7 —.03) 


(-j)z — hyp. log. ^ +1.6^ 
v = (8975.43^' + .011589)^ — .1089. 


v = (10567.8 ri + 2.67)^ — 1.64 .. 
v = (10607.02 ri + .0556)^ — .236 


v = (8976.5^/ + .012)^ — .109 
v — 140 ( ri ) a — 11 ( ri ) 5 . 


100 y r 
v = - 



v = 100 Vri 



^ 2.4 \'b' 

1 + p 


Feeder 

Chazilly.* 

Lauter 

Canal.+ 

-f 4- 

w 

z 

►H 

a 

cn 

ctn 

1 ac 

H-l u 

. « 

^ 0 
£ 

Com- 

Com- 

Com- 

Com- 

puted pitted 

puted 

puted 

veloc . 

veloc. 

veloc. 

veloc. 

in ft. 

in ft. 

in ft. 

in ft. 

per 

per 

per 

per 

sec. 

sec. 

sec. 

sec. 

0.966 

i-934 

2.107 

3- J 45 

1.929 

3.627 

2.411 

2.143 

1.932 

3.184 

2.442 

2.382 

1.109 

2.289 

1.572 

1.517 

1.962 

3-352 

2-545 

2.479 

1.932 

3.184 

2-435 

2 418 

2.161 

3-695 

2.778 

2.706 



-tf 


2.151 

3-338 

2.691 

2.627 

2.151 

3438 

2.691 

2.627 

2.151 

3-438 

2.691 

2.627 

1.047 

2.086 

2.166 

2.582 

1-237 

1-747 

2-350 

3.268 

1-372 

2.078 

2.642 

4-582 


* Feeder Chazilly. Area, 11.3 sq. ft. Hydraulic mean depth, 1.04 ft. Inclination, .000445. 
Observed velocity, 0.962 ft. 

t Lauter Canal. Area, 564 sq.ft. Hydraulic mean depth, 1.82ft. Inclination, 000664. 
Observed velocity, 2.106 ft. 

X Seine. Area, 1978 sq. ft. Hydraulic mean depth. 5.70 ft. Inclination, .000127. Ob¬ 
served velocity, 2.094 ft. 

§ B. La Fourche. Area, 3738 sq. ft. Hydraulic mean depth, 15.7 ft. Inclination, .000044. 
Observed velocity, 3.076 ft. 










































VELOCITIES OF GIVEN FILMS. 


311 


In tlie preceding table, tlie symbols in the formulas have 
values as follows: 

r = hydraulic mean depth, in feet. 

i = inclination of surface in straight channel, in feet. 

I = length, in feet. 

h" = head, or fall in the given length, in feet. 

S — sectional area of stream, in square feet. 

C = wetted solid perimeter, in feet. 

v = mean velocity of stream, in feet per second. 

In the Humphreys and Abbotts’ formula, the symbols 
have values as follows: 

a = sectional area of stream, in square feet. 

b = a function of depth = — ——— 

Vr + 1.5 

p = wetted perimeter. 

r — mean hydraulic depth. 

i — inclination of surface of stream, corrected for bends. 

W = width of stream. 

v 1 = value of first term in the expression for v. 

v = mean velocity of stream. 

330. Velocities of Given Films.—Since the chief 
source of resistance to flow arises from the reactions at the 
perimeter of the stream, along the bottom and sides, A, Z7, 
B\ A ', Fig. 51, and in a small degree along the surface 
A, A', in contact with the air, it is evident that the points 
of minimum velocity will be along the solid perimeter, and 
the point of maximum velocity will be that least influenced 
by the resultant of all retarding influences. In a channel 
of symmetrical section, the point of maximum velocity 
should be, according to the above hypothesis, on a vertical 
line passing through the centre of the section and a little 
below tlie water surface, provided the surface was unin- 




312 


FLOW OF WATER IN OPEN CHANNELS. 


fiuenced by wind. The velocity measurements of Darcy 
and Bazin* with an improved “Pitot” Tube, locate the 
thread of maximum velocity in a trapezoidal channel, at a , 
Fig. 51; a nearly concentric film of lesser velocity at b , and 
other films, decreasing regularly in velocity, at c, d, e, f, 
and g. 

If the velocities, at the depths at which the given films 
cross a vertical centre line, are plotted as ordinates from a 
vertical line, as at a , 5, c, etc., Fig. 52, their extremities will 
lie in a parabolic curve, and the degree of curvature will be 
less or greater as the velocity is less or greater, and as the 
bottom is smoother or rougher, for the given section. 
Velocity ordinates, plotted in the same manner for any 
horizontal section, as in the surface, or through b , a , b , c, 
etc., Fig. 51, will also have their extremities from shore 


Fig. 51. Fig. 52. 



nearly to the centre in parabolic curves, the longest ordi¬ 
nate being near the centre of breadth of the canal, and the 
two side parabolas being connected by a curve more or less 
flat, according to breadth of canal. In Fig. 51, d indicates 
the film of mean velocity, and it cuts the central vertical line 
at nearly three-fourths the depth from the surface. In 
deep streams, or channels in earth, it is usually a little 
below the centre of depth. 

* Tome XIX des Memoires presentes par divers Savants a lTnstitut Impe¬ 
rial de France, Planclie 4. 





























SURFACE VELOCITIES. 


313 


331. Surface Velocities.- -The velocity of the centre 
of the surface, in symmetrical channels, or of the mid- 
channel in unsymmetrical sections, is that most readily 
obtainable by simple experiment. 

For such velocity observations a given length, say one 
hundred feet of the smoothest and most symmetrical 
straight channel accessible is marked off by stations on 
both banks, and a wire stretched across at each end at 
right angles to the axis of the channel. Thin cylindrical 
floats are then put in the centre of the stream a short dis¬ 
tance above the upper wire, by an assistant, and the time 
of their passing each wire accurately noted. 

A transit instrument at each end station is requisite for 
very close observations. A small gong-bell, on a stand or 
post beside the transit, is to be struck by the observer the 
instant the centre of the float passes the cross-hair, or a 
signal is to be transmitted by an electric current, and the 
time, noted to the nearest quarter-second by a skillful 
assistant, is to be recorded. 

The floats are sometimes of wax, weighted until its 
specific gravity is near unity ; sometimes a short, thick vial, 
corked, and containing a few shot or pebbles; and some¬ 
times a thin slice of wood cut from a turned cylinder, which 
for small channels may be two inches diameter. For large 

rivers, the float may be a short keg, with both heads in 

* ' 

place, and weighted with gravel stones. The float is to be 
loaded so its top end will be just above the surface of the 
water. In broad streams, a small flag may be placed in the 
centre of the float. 

If a number of floats are started simultaneously at 
known distances on each side of the axis of the channel, 
they should have each a special color-mark or conspicuous 
flag number, so that the time and distance from axis, at 


314 


FLOW OF W T ATER IN OPEN CHANNELS. 


each station, may be correctly noted for each individual 
float. 

Du Buat made experiments with small rectangular and 
trapezoidal channels of plank, 141 feet long and about 
18 inches wide, with depths from .17 to .895 feet, and veloc¬ 
ities from .524 to 4.26 feet, to determine the ratio of the 
mean velocity v of the channel section to its central surface 
velocity, V. From the mean results he deduced the empir¬ 
ical formula of mean velocity, 

v = (VT— .15) 2 + .02233. (11) 

This gives, when V is taken as unity, 

v = .745 V. 


Prony afterwards, reviewing the same experimental re¬ 
sults, proposed the formula, 


~/F + 7.782\ 
* _ T V V + 10.345/ 



Ximenes’ experiments upon the River Arno, Raucort’s 
upon the Neva, Funk’s upon the Wesser, Defontaines and 
Brunning’s upon the Rhine, on larger scales, gave mean 
velocities in a vertical line at the centre equal to .915 V y 
which being the maximum velocity in its horizontal plane, 
indicates, if the reduction of velocity toward the shore is 
considered, an approximate mean velocity, 

7) = .915 (.915 V) = .837 V. (13) 

Mr. Francis’ experiments in a smooth, rectangular chan¬ 
nel, with section about 10 feet broad and 8 feet deep, and 
velocity of 4 feet per second, indicates 

v = .911 V. (14) 

In the Mississippi River, with depths exceeding one 



RATIOS OF SURFACE TO MEAN VELOCITIES. 315 

hundred feet, Messrs. Humphreys and Abbott occasionally 
found v greater than V. 

The Ganges Canal experiments at Roorkee, in 1875, by 
Capt. Cunningham, R. E., in a rectangular section 9 feet 
deep and 85 feet wide, gave the mean surface velocity 
equal to .927 V. 

In any series of rectangular channels of like constant 
sectional areas or of like constant borders, it is seen, by 
simple mathematical demonstrations, that the hydraulic 

mean depth — ^ r , is at its maximum when the breadth 

equals twice the depth.* Since the velocity of flow in a 
series of rectangular channels is nearly proportional to the 
square roots of their hydraulic mean depths, it follows that 
the proportions of such channels most favorable for high 
velocities is breadth equal twice depth. 

These proportions of breadth to depth being adopted 
again for another series of rectangular channels of varying 
section, the velocities will again be sensibly proportional to 
the square roots of their hydraulic mean depths. 

The ratio of v to V should be at its maximum when 
breadth equals twice the depth, and when the section is the 
maximum of the given series. 

332. Ratios of Surface to Mean Velocities.—Let 
d — depth and b = breadth of rectangular channels, then 
letting depth be unity for a depth of 8 feet and approxi¬ 
mately between 6 and 12 feet, and we shall have, according 
to the various recorded experiments, approximate values 
of the mean velocity ?; of flow in the channel, as compared 
with the central surface velocity V, as follows, for smooth 
channels: 


* Tlie influence of sectional profile upon flow is elaborately discussed by 
Downing, in Elements of Practical Hydraulics, p. 204, et seq. (London, 1875.) 




316 


FLOW OF WATER IN OPEN CHANNELS. 


When 

b = 

2d 

then 

V = 

.920 V 

u 

b = 

M 

66 

V — 

.910 V 

66 

b = 

4 d 

66 

V = 

.896 V 

66 

b = 

5d 

66 

V = 

.882 V 

66 

b = 

6d 

66 

V = 

.804 V 

66 

b = 

Id 

66 

V = 

.847 V 

66 

b --= 

8 d 

66 

V = 

.826 V 

66 

b = 

9 d 

66 

V = 

,804 V 

66 

b = 

10<Z 

66 

V = 

,780 V 



The values of v should be slightly less for trapezoidal 
canals of equal sections, decreasing as the side slopes are 
flattened. The values of v will decrease also as the bottom 
and sides increase in roughness. The wind may enhance 
or retard the surface motion, and thus affect the mean 
velocity. 

Since inclination of water surface, section of stream, 
hydraulic mean depth, and roughness of bottom and side, 
all affect the final result of flow, it is evident that experi¬ 
ence and good judgment will aid materially in the selection 
of the proper ratio of v to V. A misapplication of formulae 
that are valuable when judiciously used, may lead to gross 
errors; as, for instance, Prony’s formula, deduced from 
experiments with Du Buat’s small canal, gave result fifteen 
per cent, too small when tested by the flow in the Lowell 
flume, 10 feet wide and 8 feet deep, wdiere the volume was 
proved by tube floats and weir measurements at the same 
time. 

333. Hydrometer Hangings. — When opportunity 
offers, the mean velocity for the whole depth should be 
measured, and thus some of the uncertainties accompany¬ 
ing surface measures be eliminated. Among the most 
reliable hydrometers that have been used for this purpose 



TUBE GAUGE. 


317 


in canals and the smaller rivers may be mentioned, tin tubes 
of length nearly equal to the depth of the stream; improved 
“ Pitot tubes / ” and “ Woltmann tachometers .” 

334. Tube Gauge. —When the velocity measurements 
are to be taken with Francis’ tubes or Krayenlioff poles, 
Fig. 53, a straight section of the stream is chosen, with 
smooth symmetrical channel, clear of weeds and obstruc¬ 
tions. A length of one hundred or more feet, according to 
circumstances, is marked off by stations at each end on 
each bank, located so as to mark lines at right angles to the 
axis of the stream. A steel measuring chain, or wire with 
marks at equal intervals, is then to be stretched across at 
each end. The depths are then to be taken across the stream 
at each end, and at the centre if the banks are warped, at 
known intervals of a few feet, accord¬ 
ing to the formation of the banks and 
bottom of the stream, so that the sec¬ 
tional area of the stream shall be 
accurately known, and may be plot¬ 
ted. The soundings are all to refer 
to the same datum previously estab¬ 
lished, and referred to a permanent 
bench mark on the shore, which will greatly facilitate 
future observations or verifications at the same point. 

The requisite number of tight tin tubes, of say two 
inches diameter,* are then to be prepared, one for the axis 
of the stream, and others for short successive intervals on 
each side of the axis, all to be duly numbered for their 
respective positions. The length of each is to be such that 
it will float just clear of the bottom, and extend to a little 
above the water surface. The tube is to be loaded at one 

* Tabes 40 feet long, 3 inches diameter, made up in sections, have been 
used by the United States Coast Survey Staff. 


Fig. 53. 



















318 


FLOW OF WATER IN OPEN CHANNELS. 


end with fine shot or sand, until it has the proper sub¬ 
mergence in a vertical position, .93 to .95 depth. 

The several tubes are to be started by signal, simultane¬ 
ously if possible, from a short distance above the upper end 
station, so that they may cross the upper station as nearly 
as possible at the same instant. Their arrivals at the lower 
stations are to be carefully noted, and the time of transit of 
each recorded. 

When the experiment has been several times repeated, 
the central and other tubes may be passed down singly, if 
the volume of the stream still remains constant, to verify the 
first observations. In the last observations, transits may 
conveniently be used to observe the passage by the stations, 
as suggested above for observing surface floats. 

. Suppose the stream to be divided transversely into seven 
sections, as in Fig. 54, then tubes 1, 2,3, etc., may be started 


Fig. 54. 



in the centres of their respective sections. The degree of 
accuracy with which they will move along their intended 
courses will depend upon the symmetrical regularity of 
flow, and very much upon the regularity of the side banks, 
and several trials may be necessary to get satisfactory 
side and even central measurements,’ since a slight obstruc¬ 
tion, or a stray boulder upon the bottom, may distort the 
fluid threads in an unaccountable manner. The side floats 
have also a tendency away from shore. 

The mean area of each of the sub-sections being known, 
and the mean velocity through each being ascertained. 


















GAUGE FORMULAS. 


319 


their product gives the volume flowing through, and the 
sum of volumes of the sub-section gives the volume for the 
whole section. 

When streams are in the least liable to fluctuations from 
the opening or closing of sluices above, or the opening or 
closing of turbine gates when the stream is used for hy¬ 
draulic power, a hook-gauge (Fig. 48), should be placed 
over the axis of the stream where the usual vibration of 
surface is least, to watch for such fluctuations, since a vari¬ 
ation in the mean level of the water surface one-liundredtli 
of a foot will appreciably affect the velocity and volume of 
flow. If the tubes have much clearance they will not be 
influenced by the films of slowest velocity next the bottom. 
A clearance of six inches in a rectangular flume eight feet 
deep, may give an excess of three per cent, of velocity. 
The cross-section depths, in canals and shallow streams, 
may be taken with a graduated sounding-rod having a flat 
disk of three or four inches diameter at its foot, and in deep 
streams by a measuring-cliain with a sufficient weight upon 
its foot to maintain it straight and vertical in the current. 
A good level instrument and level staff are requisite, how¬ 
ever, for accurate work. 

In broad streams the transverse stations may be located 
trigonometrically by two transits placed at the extremities 
of a carefully measured base line upon the shore. 

335. Gauge Formulas. —The volume of flow through 
the mean transverse section (Fig. 54) is required. 

Let s be the established length , or distance between the 
longitudinal end stations, and U 4 U • • • • L the times occu¬ 
pied by the several tubes in passing along their respective 
courses between end stations; then the mean velocities in 
the respective sub-sections will be 

s s s s 

J— — j J~ — V 2 , JT ^3 5 ••••/“ — Vn* 

(y{ C-2, t'3 t/ n 


320 


FLOW OF WATER IN OPEN CHANNELS. 


Let tlie transverse breadths of the sub-sections be, a, ct 2 a 3 • • • • Ct^n. 
“ “ mean depths “ “ “ “ d 1 d 2 d 3 . . . . d n . 

“ “ mean velocities in “ “ “ v x v 2 v 6 ... . v n . 

“ “ “ volumes of flow in “ “ q l q 2 q 3 . . . . q n . 


Then the whole sectional area in square feet, S, of the 
stream is, 

S = . dt + a 2 . d 2 + a 3 . d s 4- . . . . a n . d n ; (16) 


and the whole volume in cubic feet, Q , is 


Q = (a x . d { ) v i + (a 2 . d 2 ) v 2 + (a 3 .d 3 )v 3 + ... (a n . d „) v n ; (17) 

and the mean velocity in feet per second, v , of the whole 
section is, 




The summary of field notes, beginning at a on the left 
shore, is: 



Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 


Breadths of sub-sections 

a x 16.45 

a. 2 20,00 

a 3 24.85 

a. a2.oo 

a.3 29.50 

a a 26.80 

a 7 18.24 


Mean depths of “ 

Mean velocities in the I 
sub-sections. f 

di 4.85 
v, 2.25 

d 2 9.74 
v 2 3.80 

d 3 12.37 
V3 4.62 

d t 15.68 

d s 12.52 

v 5 4-65 

d e 9.71 

d i 4-79 

v< 5.00 

v a 3.75 

v 7 2.00 


Volume in the sub-sec- 1 
tions.j 

Cu. ft. 

Cu. ft. 

Cu.ft. 

Cu.ft. 

q. 2508.8 

Cu. ft. 

Cu. ft. 

< 7 « 975-8 

Cu. ft. 

L<?- 

<7 1 179-5 

q-i 740-2 

? s 1420.2 

< 7 si 7 W -4 

q 1 174-7 


The sum of the several products of breadth into depth is 
S = 1800.675 square feet. 

The sum of the several volumes is. Q = 7716.73 

The mean velocity for the whole section is ^ 

o 1800.075 

= v = 4.285 feet per second. 

If the tubes have several inches clearance at the bot¬ 
tom, a slight reduction, say two and a half per cent,, from 
the computed velocity and volume are to be made, to com¬ 
pensate therefor. 

336. Pitot Tube Gauge. —The Pitot tube has been 
used with a tolerable degree of success in many experi¬ 
ments upon a small scale. In its best simple form it has 




















PITOT’S TUBE. 


321 


been constructed of glass tubing swelled into a bulb near 
one end, and with tube of smaller diameter below the bulb 
bent at a right angle, and terminated with an expanded 
trumpet-mouth, as in Fig. 55. 

For deep measures the mouth and bulb and a con¬ 
venient part of the tube may be of copper, that part which 
is to project above the surface 
of the water being of glass, and 
the whole instrument may be at¬ 
tached to a vertical rod, which 
rests on the bottom, so as to be 
slid up and down on the rod to 
the heights of the several films 
whose velocities are required. 

When in use, the bulb and 
tube are to be held vertically, 
and the small trumpet-mouthed 
section exposed horizontally to the current so as to receive 
its maximum force into the mouth. 

The object of the expanded bulb and contraction below 
the bulb is to reduce oscillation of the water within the tube 
to a minimum. 

Theoretically the impulse of the current, acting as pres¬ 
sure on the water within the tube, should raise the surface 


Fig. 55. 



55 

pitot’s tube. 


of the water within, a height, Ji = 


v 2 


above the normal 


surface. 

But owing to reactions from several parts of the tube, 
the entire force of the current does not act upon the column 
of water in the vertical section of the tube, lienee the eleva¬ 
tion of the water in the tube is cji and 


7) 2 

%/ 


= cji and v 


V2ycji. 



21 


















322 


FLOW OF WATER IN OPEN CHANNELS. 


The coefficient c of for tlie given tube and tlie different 
velocities, must be determined by experiment before it can 
be used for practical measures. 

The stream is cross-sectioned, as before described for 
the leading station when long tin tubes are used, and 
the mean velocity is ascertained from the mean velocity of 
the various superposed films taken in a vertical line at the 
centre of each sub-section. 

The computations of volume are made in a manner sim¬ 
ilar to those when tubes are used. 

Pitot introduced a plain tube bent at right angles as 
early as 1730, and by his measurements with it in the Seine 
and other streams, overthrew some of the hypotheses of the 
older liydraulicians. 

It has since received a variety of forms and entered into 
a variety of combinations, among which may be mentioned 
the “ Darcy-Pitot ’ ’ tube, which, after an instantaneous 
closing of a stop-cock, can be lifted up for an observation, 
and the Darcy double tube, but there is still difficulty in 
reading by its graduations measures of small velocities,with 
sufficient accuracy, and the capillarity may be a source of 
error in unskillful hands. 

The almost exclusive use of this instrument in improved 
forms by Darcy and Bazin in their valuable series of ex¬ 
perimental observations, has given to it prominent rank 
among hydrometers. 

337. Woltmann’s Tachometer.— The most success¬ 
ful of all the simple mechanical hydrometers, not requiring 
the assistance of an electric battery, has been the revolving 
mill introduced by Woltmann in 1790, and known as 
u Woltmanwb s Tachometer ,” or moulinet. This current 
meter has from two to five blades, either flat or like marine 
propeller blades, set upon a horizontal shaft as shown in 


WOLTMANN’S TACHOMETER. 


323 


Fig. 56, which represents the entire instrument * in its actual 
magnitude, for small canal and flume measures. 

Upon the main axle, which carries the propeller, is a 
worm-screw, G. A series of toothed wheels and pinions, 
with pointers and dials similar to the registering apparatus 


Fig. 56. 



woltmann’s tachometer. 


of a water or gas meter, are hung in a light frame, C, imme¬ 
diately beneath the main axle. One end of the frame is 
movable upward and downward, but when out of use is 
held down by a spring, F. 

The whole instrument is secured by a set-screw upon an 
iron rod, I), on which it may be set at any desired height. 


* Another form with two blades is illustrated in Stevenson’s Canal and 
River Engineering. Edinburgh, 1872, p. 101. 

























































324 


FLOW OF WATER IN OPEN CHANNELS. 


When brought into practical use, the instrument is 
adjusted upon the rod,* so that when the staff rests upon 
the bottom, the main axle will be at the height of the film 
to be first measured. It is then placed in position with the 
propeller toward the approaching current and the main axle 
parallel with the direction of the current. The propeller 
will soon acquire its due velocity of revolution from the 
moving current, when the movable end of the frame carry¬ 
ing the recording train is lifted by the wire E, and the first 
toothed wheel brought into mesh with the worm-screw. If 
the train does not stand at zero, its reading is to be taken 
before the instrument is brought into position. The times 
when the train is brought into mesh with the worm-screw, 
and when disengaged, are both to be accurately noted and 
recorded. 

Upon the slackening of the wire E, the spring E, in¬ 
stantly thrown the train out of mesh, and it is held fast by 
the stud A, which engages between two teeth of the wheel. 
The instrument may then be raised and the revolutions in 
the observed time read off. In waters exceeding a few feet 
in depth there are usually pulsations of about one minute, 
more or less, intervals, and the instrument should be held 
in position until several of these have passed. 

The velocities are thus measured at several heights on 
vertical centre lines in the several sub-sections, and the com¬ 
putations for mean velocity and volume completed as in the 
above described case when long tin tubes are used. 

The blades of the propeller are usually set at an angle 
of about 70°, or with an equivalent pitch if warped as a pro¬ 
peller blade. 


* Several moulinets upon the same staff, at known heights between bottom 
and surface, expedite the work and tend to greater accuracy. 



HYDROMETER COEFFICIENTS. 


325 


338. Hydrometer Coefficients. —The number of revo¬ 
lutions of the main axle is nearly proportional to the velocity 
of the impinging current; but there is some frictional resist¬ 
ance offered by the mechanism, hence it is necessary that 
the coefficients for the given instrument and for given veloci¬ 
ties be established by experiment, and tabled for convenient 
reference before it is put to practical use. These coefficients, 
which decrease in value as the velocity increases, may be 
ascertained, or verified, by placing the instrument sub¬ 
merged in currents of known velocity, or by causing it to 
move, submerged, through still water at known velocities. 

An apparatus adapted to the last purpose is described 
by L’ Abbe Bossut, and illustrated in Plates I and II, in 
“ Experts * De Bossut,” 

If the instrument is to be tested in a reservoir of still 
water, by moving it with different known velocities through 
a given distance, let s be that distance, t the time consumed 
in passing the instrument from end to end stations, n the 
number of revolutions of the main axle in the given time t , 
c 0 the coefficient of revolutions for the given velocity, and v 
the given velocity. 

Then 4 = v ; and — = c Q : and c 0 n = s ; and = v. 
t n ’ ^ 

Now if the instrument is placed in a current, and n is 
the observed number of revolutions in the given time, c 0 may 
be taken from the table, or an approximate value of c 0 as¬ 
sumed and nearer values determined by the formula 

^ = c 0 , when the velocity will be, v = (20) 

* Nouvelles Experiences sur la Resistance des Fluids ; M. TAbbe Bossut, 
Rapporteur. Paris. 

Vide, also, Annales des Ponts et Chaussees, Nov. et Dec., 1847, and Journal 
of Franklin Institute, May, 18S9, and Beaufoy’s Hydraulic Experiments. 





325a 


FLOW OF WATER IN OPEN CHANNELS. 


When an electric register is used, one minute observa¬ 
tions, between the starting and stopping of the recorder, 
gives revolutions per minute direct, and for other times 

their ratio r = j , in which t x is in minutes. From this 

ratio, velocity y = v of flow in feet per second is desired, 
and equals 

* y = cx+m , (20a) 

in which x is the revolutions per minute and m the small 
portion of velocity balancing friction of the meter mech¬ 
anism. 

A series of trial tests are to be made for rating each 
meter, on the same base line, in still water, and these sev¬ 
eral values are found from the experiments, thus: 


TABLE No. 76a. 

Current Meter Rating Experiments. 


j 

a 

o 

a 

• H 


0) 

a 

x 




<u 

i/i 


m 


o 

6 

Z 


bn 

a 

ci 





J) 

. 

c 

bn 

0 

c 


r—• 

3 O 

d 

O 3 

0 

X 

>.g 

<U A 

u 

oi a 

0 

Vh 

4-> 


C/3 

0 S, 

fc£ 


D 

c 

Pi 

z 


a 

H 


2 

3 

4 

5 

6 

7 

8 

9 

io 


^ in ft. 



min. 
— G • 



( 2115 ) 

200 

1 2161 j 

ftft 

22^6 

ft* 

2250 

<b 

2300 

ftft 

2345 

ft ft 

2397 

ftft 

2441 

ftft 

2493 

ftft 

2537 

ftft 

2589 


46 


114 


1.9000 


45 

44 

50 

45 
‘2 

44 

52 

44 

52 


ii5 

149 

35 

no 

24 

182 

27 

142 

25 


1.9167 

2- 4833 
•5833 

1 - 8333 

.4000 

3- 0333 
.4500 

2-3333 

.4166 


Coefficient. 

Observed 
Velocity in feet 
per second. 

Ratio. 

Computed Velocity. 
.0619.2; + .255 

S 

j 

c 0 = — 
n 

s 

y ~ 1 
— c ° n _ 

n 

= V. 

4 3478 

t 

1-7544 

24.211 

1.6328 

4.4444 

1 • 739 1 

23-478 

1.5863 

4-5454 

I -3423 

i 7 - 7 i 8 

1.1994 

4.0000 

5 - 7 I 43 

85.710 

5 - 74 I 5 

4-4444 

T.8181 

24-540 

1.6585 

3.8461 

8-3333 

129.000 

8.6845 

4-5454 

1.0988 

14.502 

.9820 

3.8461 

7.4074 

II 5-555 

7 • 7 J 95 

4-5454 

1.4084 

18.588 

1.2766 

3.8461 

7.9998 

124.800 

8.3384 


Having values as above, the series y may be plotted to 
scale as abscissas and the dependent coefficients c 0 and ratios 



































CURRENT METER RATING EXPERIMENTS. 


3 2ob 


r as ordinates, and more complete series taken from the 
scale. 

If the experiments are conducted with proper care and 
precision, and the meter is in proper condition, the extrem¬ 
ities of the ordinates r will be found to lie approximately 
in a straight line. 


Select from the minimum and maximum velocity values, 
representative values, and let their respective symbols be y r 
and y "; also let their respective revolution ratios have 
symbols x' and x". Then, for the equation of the series of 
ratings, we have 



_ y" - y' 

x" — X■ 


(pd — x"). 


(20 b) 


From experiments Nos. 1 and 8 of the series we have 
values, to substitute in the equation, 

y' = 1.7544, y" = 7.4074, 

x' = 24.211, x" = 115.555. 


,, 7 4fr , _ 7.4074 - 1.7544 . 

y ~ 7A074 - { 


y = .0619^ -f .255, (20c) 

in which .0619 is the coefficient for the meter tested. In 
the practical use of a meter, x is the registered revolutions 
per minute , which is to be multiplied by the coefficient of 
the given meter to obtain ?/, the velocity in feet per second 
of that thread of the current in which the meter wheel is 
revolving. 






326 


FLOW OF WATER IN OPEN CHANNELS. 


339. Electric Moulinets. —The ingenious indicating 
current meter * invented and introduced in the Lake Survey 
by I). Farrand Henry, C. E., has greatly increased the con¬ 
venience and accuracv of measurements in broad and strong 
streams and tidal estuaries, since with the aid of an electric 
battery and current the revolution recorder may be retained 
on shore, float or vessel, and one minute observations be 
repeated in alternate minutes. 

The general features of this meter are shown in the plate 
fronting this chapter. Another excellent form of meter, 
Fig. 56a, was designed by Mr. A. Fletey, resident engineer 
of the Boston additional water supply. The writer has used 
the “Price” meter, Fig. 565, with satisfactory results in 
rapid and in deep currents, and also in head and tail races of 
water powers, and found it to embody the best features of 
substantial registering current meters. 

340. Earlier Hydrometers. —Castelli’s quadrant, or 
hydrometric pendulum, Boileau’s horizontal gauge glass, 
Gauthey’s and Brunning’s pressure plates, Brewster’s long 
screw-meter, and Lapointe’s beveled gear-meter, have now 
all been superseded by the more perfect modern current 
meters. 

341. Double Floats. —Various double-float combina¬ 
tions, having one float at the surface and a second near the 
bottom, connected with the first by a cord or fine wire rope, 
have been used both in Europe and America. The liability 
of erroneous deductions from the movements of such com¬ 
binations has been ably discussed f by Prof. S. W. Rob¬ 
inson. 

342. Mid-deptli Float s.— The mid-depth float proves 


* This meter is illustrated in the Jour, of the Franklin Inst., May, 1869, 
and Sept. 1871. 

\ Vide Van Nostrand’s Eclectic Engineering Magazine, Aug., 1875. 



Fig. 50. 



IMPROVED CURRENT METERS 

3*26 











































MID-DEPTH FLOATS. 


327 


most generally satisfactory of all float apparatus, excepting 
full-deptli tubes, for gauging artificial channels and the 
smaller rivers. 

This may consist of a hollow metal globe of say six 
inches diameter, with a cork-stopper or pet-cock at its 
lower vertical pole, which permits the partial filling of the 
globe with water until its specific gravity, submerged, is 
slightly in excess of unity. This globe is connected by a 
fine flexible wire with the smallest and lightest circular 
disk-float upon the surface that can retain the globe in its 
proper mid-depth position. 

It is desirable that the float be controlled as fully as 
possible by the mid-depth velocity, where, in artificial 
channels and deep streams, the film of most constant 
velocity is found. The reactions and eddies that continually 
agitate all the particles that flow near the bottom and sides 
of the stream, and the wind pressure and motion along the 
surface, make the motions of all perimeter (so called) films 
very complex, and continually cause the parabolic velocity 
values in the central vertical plane to change between 
flatter and sharper curves, or to straighten out and double 
up, hinged, as it were, upon a mid-depth point; hence the 
bottom, side, and surface velocities are liable to great irreg¬ 
ularities, and these irregularities are projected to some 
extent through the whole body of the water. These effects 
may be readily observed in a stream carrying fine quartz 
sand, upon a sunshiny day, if a position is taken so that 
the sunlight is reflected from the sand-grains to the eye. If 
in such case the eye and body is moved along with the cur¬ 
rent, the whole mass of water appears in violent agitation 
and the particles appear to move upward, downward, back¬ 
ward, forward, and across, with writhing motions, illus¬ 
trating the method by which the water tosses up and bears 


328 


FLOW OF WATER IN OPEN CHANNELS. 


forward its load of sediment. In the midst of this agitation, 
the film having a velocity nearest to the mean resultant of 
onward progress is usually over the mid-channel of a 
straight course, and near to, or a little below, the centre of 
depth. The suspended float that takes this mean velocity 
is more certain to give a reliable velocity measure than that 
controlled by any other point of the stream section. 

343. Maximum Velocity Floats. —If it is desired to 
place the submerged float in the film of maximum velocity 
in artificial channels, then this may be sought over the 
mid-channel, and between the surface and one-third the 
depth, according to the cross-section of the stream and 
velocity of flow. In a smooth rectangular section with 
depth equal to width, or with depth one-half width, it will 
probably be near one-tliird the depth, and higher as the 
depth of stream is proportionately less, until depth is only 
one-fourth breadth, when it will have quite, or nearly, 
reached the surface. 

The film of maximum velocity may reacn the surface in 
trapezoidal canals when depth of stream is only one-third 
mean breadth. It is at one-fourth depth in the trapezoidal 
channel, Fig. 51, in which bottom breadth equals twice depth. 

In shallow streams, the maximum velocity is at or near 
the surface. 

344. Relative Velocities and Volumes due to 
Different Depths. —When the mean velocity has been 
reliably determined in a channel, or small stream, at some 
given section, and for some particular depth, it is often 
desirable to construct a table of velocities and volumes of 
flow, for other depths in the same section, so that, if a read¬ 
ing of depth is taken at any time from a gauge established 
at that section, the velocity and volume due to the observed 
depth at that time may be read off from the table. 


RELATIVE VELOCITIES AND VOLUMES. 


329 


TYIT) 4, 

The inclination, or surface slope, i = -—, and the value 

of the coefficient of friction, m = , may he observed 

within the ordinary extremes of depth at the time of the 
experimental measurement, if opportunity offers, or other¬ 
wise for the given experimental depth, and computed for 
the remaining depths. 

Theory indicates that the variation of velocity , with 
varying depth, is nearly as the variation of the square root 


of the hydraulic mean radius, 



and the variation of 


volume of flow is nearly as the variation of the product of 
sectional area into the square root of hydraulic mean radius, 



These terms are readily obtained for the several depths, 
from measurement of the channel. 

To compare new depths, velocities, and volumes, with 
the depth, velocity, and volume accurately measured by 
experiment, as unity , 


let the experimental depth be d, and the new depth he d x ; 


66 

u 

(6 

hy. mean rad. 

66 

r, 

66 

66 

66 

hy. mean rad. 

66 


66 

u 

66 

slope 

66 

i, 

66 

66 

66 

slope 

66 

h ; 

u 

66 

66 

coef. of friction 

66 

m, 

66 

66 

66 

coef. of friction 

66 

m x ; 

a 

61 

66 

sectional area 

66 

s, 

66 

66 

66 

sectional area 

66 

S t ; 

66 

66 

66 

velocity 

66 


66 

66 

66 

velocity 

66 

®i ; 

a 

66 

66 

volume 

66 

q> 

66 

66 

66 

volume 

66 

?!• 


The relative values of new depths, velocities, volumes, 


etc., will be 





h- 

v 9 


and 


v : Vi 




330 


FLOW OF WATER IN OPEN CHANNELS. 


q : :: 1 : ^; etc. 

The ratio of v x to v is 



v x j2gr 1 i 1 \i m j 2gri j r x i x rri 

v \ m i 1 ' \ m \ ~ \ rimi f 5 


and 

j Tii x m ) \ 

V x = Vi -Id—- V 

( mm x j 

(21) 


q ' = q 8v =S,V " 

(22) 


In long straight channels of uniform section, i x will be 
less than i for increased depths, and greater than i for 
reduced depths; but ordinarily (except with great velocities) 
their values will be so nearly equal to each other that they 
may be omitted from the equation without serious error, 
when the equation of velocity will become, 


v± — v 


r x m\\ 
rm x f 



The variations in m cannot be neglected in relatively 
shallow channels. 

For illustration of the equations, let Fig. 57 be a smooth 


Fig. 57. 



trapezoidal channel, 6 feet broad at the bottom, = e, and 
with side slopes inclined thirty degrees from the horizon, 
= 0 - 


































FAIRMOUNT PUMPING MACHINERY, PHILADELPHIA 

























































































































































































































































































































RELATIVE VELOCITIES AND VOLUMES. 


331 


During tlie experimental measurement, let the depth be 
4 feet; the slope, one foot in one mile = i = .000189 ; the 
experimental velocity, 1.201 feet per second; and the ex¬ 
perimental volume, 62.128 cubic feet per second. 

The velocities and volumes are to be computed when the 
depths are 2 feet and 6 feet, respectively. 

Let cl be any given depth; 

e “ the bottom breadth, = 6 feet; 
b “ the mean breadth ; 

<P “ the slope of the sides, = 30°; 

JS “ the sectional area ; 

C “ the wetted earth perimeter. 

Then we have for the given values of d: 


Assumed Values of d. 

2 Feet. 

4 Feet. 

6 Feet. 

. 2 d 




b — e + --— ... — 

tan cb 

I2 -9 3 

19.86 

26.79 

d 2 




S =-f- de .. = 

tan c f > 

i8 -93 

5 1 -73 

9 8 - 3 S 

2 d sec 4> 




C—e + -x" = 

tan tb 

14.00 

22.00 

30.00 

s 




r C . 

i -35 

2.30 

3 . 28 


.0002 

.000189 

.OOOI85 

m .— 

.02396 

.0187 

.OI46 

v x ..\ .= 

.836 

1.201 

I.606 

.= 

i 5- 82 5 

62.128 

r 57 - 9 S 


With increase of depth, there is also increase of velocity; 
hence there are two factors to increase of volume. 

Some practical considerations relating to open canals 
are given in Chap. XVII, following. 






















Fig. 58. 



I 


DISTRIBUTING RESERVOIR. 












































































































SECTION III. 


Practical Construction of Water-works, 


CHAPTER XYI. 

RESERVOIR EMBANKMENTS AND CHAMBERS. 

345. Ultimate Economy of Skillful Construction. 

4 

—An earthwork embankment appears to the uninitiated 
the most simple of all engineering constructions, the one 
feature that demands least of educated judgment and expe¬ 
rience. Possibly from such delusion has, in part, resulted 
the fact, which is patent and undeniable, that failures of 
reservoir embankments have exacted more terrible and 
appalling penalties of human sacrifice, and sacrifice of cap¬ 
ital, than the weaknesses of all other hydraulic works 
together. 

Each generation in succession has had its notable flood 
catastrophes, when its broken dams have poured deluges 
into the valleys, which have swept away houses and mills 
and bridges and crops, and too often twenty, fifty, or a 
hundred human beings at once. 

Such devastations are scarcely paralleled by,' though 
more easily averted by forethought, than those historical 
inundations when the sea has broken over the embanked 
shores of Holland and England, and when great rivers 



334 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


have poured over their populous leveed plains, yet they 
seem to be quickly forgotten, except by the immediate 
sufferers who survived them. 

The earliest authenticated historical records of the East¬ 
ern tropical nations describe existing storage reservoirs and 
embankments, and more than fifty thousand such reser¬ 
voirs have been built in the Indian Madras Presidency 
Districts alone. Arthur Jacobs, B. A., says* of these 
Madras embankments, that they will average a half mile in 
length each, and the longest has a length of not less than 
thirty miles. 

Two thousand years of practice seems to have developed 
but a slight advance of skill in the construction of earth¬ 
works, while their apparent simplicity seems to have dis¬ 
tracted modern attention from their minute details, and to 
have led builders to the practice of false economy in some in¬ 
stances, and to the neglect of necessary precautions in others. 

Among the recent disastrous failures may be mentioned 
the Bradfield or Dale Dyke embankment of the Sheffield, 
England, water-works, in 1864 ; the Danbury, Conn., water¬ 
works embankment, in 1866 ; the Hartford, Conn., water¬ 
works embankment, in 1867 ; the New Bedford, Mass., 
water-works embankment, in 1868; the Mill River, or 
Williamsburgli, Mass., embankment, in 1875 ; and Worces¬ 
ter, Mass., water-works embankment, in 1876. More than 
one hundred other breakages of dams are upon record for 
New England alone for the same short period. 

The practical utility of streams is dependent largely 
upon the storage of their surplus waters in the seasons of 
their abundant flow, that they may be used when droughts 
would otherwise reduce their volume. 


* Vide Paper read before the Society of Engineers, London. 



EMBANKMENT FOUNDATIONS. 


335 


Tlieir waters are usually stored in elevated basins, 
whether stored for power, for domestic consumption, for 
compensation, or to regulate floods; and frequently single 
embankments toward the head-waters of streams suspends 
millions of tons of water above the villages and towns of 
the lower valleys. In other instances, embanked distrib¬ 
uting reservoirs crown high summits in the midst of popu¬ 
lous cities. These are good angels of health, comfort, and 
protection, when performing their appointed duties,, but 
very demons of destruction when their waters break loose 
upon the hillsides. 

Every consideration demands that a storage reservoir 
embankment shall be as durable as the hills upon which it 
rests. To this end, no water is to be permitted to percolate 
and gather in a rill beneath the embankment; its core must 
be so solid, heavy and impervious that no w T ater shall push 
it aside, lift it up or flow through it, or follow along its dis¬ 
charge pipes or waste culvert; its core must be protected 
from abrasions and disintegrations; and its waste overfall 
must be ample in length and strength to pass the most 
extraordinary flood without the embankment being over¬ 
topped. 

346. Embankment Foundations. —The foundation 
upon which the structure rests is the flrst vital point requir¬ 
ing attention, and may contain an element of weakness that 
shall ultimately lead to the destruction of the structure 
placed upon it. 

The superposed drift strata beneath the surface layer of 
muck or vegetable soil may consist of various combinations 
of loam, gravel, sand, quicksand, clay, shale and demoral¬ 
ized rock, resting upon the solid impervious rock, or above 
an impervious stratum of sufficient thickness to resist the 
penetration of water under pressure. If the water is raised 


336 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


fifty feet above the surface and there are thirty feet of per¬ 
vious earth in the bed of the valley, then the pressure upon 
the bed stratum will be five thousand pounds, or two and 
one-lialf tons per square foot, which will tend to force the 
water toward an outlet* in the valley below. That much of 
the natural earth is porous is well demonstrated by the 
freedom with which water enters on the plains and courses 
through the strata to the springs in the valleys, even with¬ 
out a head of water to force its entrance. Such porous 
strata must be cut off or sealed over, or the permanency and 
efficiency of the structure, however well executed above, 
cannot be assured. 

If the valley across which the embankment is thrown is 
a valley of denudation, or if the embankment stretches 
across one or more ridges to cover several minor valleys 
with a broad lake, the waters in rising may cover the 
outcropping edges of coarse porous strata that shall lead 
the fiowage by subterranean paths to distant springs where 
water had not flowed before. Hence the necessity of a 
thorough examination of the geological substructure of 
the valley, and of tests by trial shafts, supplemented by 
deep borings, of the site of the embankment and the hill¬ 
sides upon which it abuts. The test borings should cover 
some distance above and below the site of the embankment, 
lest a mere pocket filled with impervious soil be mistaken 
for a thick strata supposed to underlie the whole vicinity. 

The trial shafts only, permit a proper examination of the 
covered rock, which may be so shattered, or fissured, as to 
1 be able to conduct away a considerable quantity of water, 
or to lead water from the adjoining hills to form springs 
under the foundations. 

Several deep reservoirs constructed within a few years 
past have demanded excavations for cut-off walls, to a 


SURFACE SOILS. 


337 


deptli of a hundred feet at certain points along their lines, 
but the porosity and the firmness of the strata in such cases 
are points demanding the exercise of the most mature judg¬ 
ment, that the work may be made sure, and at the same 
time labor be not wasted by unnecessarily deep cutting. 

Thoroughness in the preliminary examination of the 
substrata of a proposed site may frequently result in the 
avoidance of a great deal of vexatious labor and enhanced 
cost that would otherwise follow from the location of an 
embankment over a treacherous sub-foundation. 

347. Springs under Foundations. —If the excava¬ 
tion shall cut off or expose a spring that, when confined, 
will produce an hydrostatic pressure liable to endanger the 
outside slope of the embankment, it must be followed back 
by a drift or open cutting to a point from whence it may 
be safely led out in a small pipe below the site of the 
embankment. 

348. Surface Soils. —Dependence cannot be placed 
upon the vegetable soil lying upon the site of an embank¬ 
ment to hold water under pressure, for it is always porous 
in a state of nature, as is also the Subsoil to the depth pene¬ 
trated by frost. The vegetable soil should be cleared from 
beneath the core of the embankment, and the subsoil rolled 
and compacted. 

The vegetable soil will be valuable for covering the top 
and outside slope of the embankment. 

If good hard-pan underlies the surface soil to a depth 
sufficient to make a strong foundation for the embankment, 
then its surface should be broken up to the depth it has 
been made porous by frost expansion, and the material 
rolled down anew in thin layers with a grooved roller of 
not less than two tons gross weight, or of one-half ton per 
lineal foot. 


22 


338 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


If next to the surface soil there is a layer of hard-pan 
within the basin to be flowed, and this hard-pan covers open 
and porous strata that extend below the dam, caution 
should be used in disturbing the hard-pan, lest the water 
be admitted freely to the porous strata, when it will escape, 
perhaps by long detour around the dam. 

341), Concrete Cut-off Walls. —If the trench for the 
cut-off wall is deep and very irregular, it is well to level up 
in the cuts with a water-proof concrete well settled in place, 
and this may prove more economical than to cut the deep 
trench of sufficient width to receive a reliable puddle wall; 
also, the greater reliability of the concrete under great pres¬ 
sure should not be overlooked. 

350. Treacherous Strata.— In one instance the writer 
had occasion to construct a low embankment, not exceed¬ 
ing twenty feet height at the centre, across an abraided cut 
through a plain. The embankment was to retain a storage 
of water for a city water supply, and the enclosed lake was 
to have an area of 200 acres. 

The test pits and soundings developed the fact that the 
abraided valley and adjacent plains were underlaid with a 
stratum of fine sand twelve feet in thickness, which, when 
disturbed, became a quicksand, and if water was admitted 
to it, would flow almost as freely as water. 

The sand lay in a compact mass, and would not pass 
water freely until disturbed. Above the sand was a layer 
of about three feet of fine hard-pan, and above this about 
three feet of good meadow soil had formed. 

For this case the decision was, not to uncover the quick¬ 
sand, but to seal it over in the vicinity of the embankment. 
The foundation of the embankment, and of the waste over- 
fall which necessarily came in the centre of length of the 
embankment, was made of concrete of such thickness as to 


EMBANKMENT CORE MATERIALS. 


339 


properly distribute the weight of the earthwork and over- 
fall masonry. Above the embankment, after a careful 
cleaning of the soil to the depth penetrated by the grass 
roots, the valley was covered with a layer of gravel and 
clay puddle for a distance of one hundred feet. 

Beneath the toe of the inside slope, where the bottom 
puddle joined the concrete foundation, a trench was cut 
’ across the valley into the quicksand, as deep as could be 
excavated in sections, with the aid of the light pumping 
power on hand, and sheet piling placed therein and driven 
through the quicksand, and then the trench was filled 
around the piling with puddle, thus forming a puddle and 
plank curtain under the inside edge of the embankment. 

Such expedients are never entirely free from risks, 
especially if a faithful and competent inspector is not re¬ 
tained constantly on the work to observe that orders are 
obeyed in the minutest detail. 

In the case in question many thousands of dollars were 
saved, and the work has at present writing successfully 
stood the test of seven years use, during which time the 
most fearful fiood storm recorded in the present century has 
swept over the section of Connecticut where the storage lake 
is situated. 

351. Embankment Core Materials. — Rarely are 
good materials found ready mixed and close at hand for 

the construction of the core of the embankment. It is 

% 

essential that this portion be so compounded as to be im¬ 
pervious. 

If we fill a box of known cubical capacity, say one cubic 
yard, with shingle or screened coarse gravel, we shall then 
find that we can pour into the full box with the gravel a 
volume of water equal to twenty-eight or thirty per cent, 
of the capacity of the box, according to the volume of voids; 


340 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


or if we attempt to stop water with t-lie same thickness (one 
yard) of gravel, we shall lind that water will How through 
it very freely. Then let the same gravel be dumped out 
upon a platform and twenty-eight per cent, nearly of line 
gravel be mixed with it, so as to till the voids equally, and 
the whole be put into the measuring-box. We now find 
that we can again pour in water equal to about thirty per 
cent, of the cubical measure of the tine gravel. Then let fine 
sand, equal to this last volume of water, be mixed with the 
coarse and fine gravel, and the whole returned to the meas¬ 
ure. We now find that we can pour in water, though not 
so rapidly as before, equal to thirty-three per cent, approx¬ 
imately of the cubical measure of the sand, and we resort 
to fine clay equal to the last volume of the water to again 
fill the voids. The voids are now reduced to microscopic 
dimensions. 

If we could in practice secure this strict theoretical pro¬ 
portion and thorough admixture of the material, we should 
introduce into one yard volume quantities as follows: Coarse 
gravel, 1 cubic yard ; fine gravel, 0.28 cubic yard; sand, 
0.08 cubic yard ; and clay, 0.03 cubic yard, or a total of 
the separate materials of 1.39 cubic yards. 

In practice, with a reasonable amount of labor applied 
to thoroughly mix the materials so as to fill the voids, we 
shall use, approximately, the following proportion of ma¬ 
terials : 


Coarse gravel. 


Fine gravel. 


4 4 4 € 

Sand. 


<t u 

Clay. 


4 4 4 4 

Total. 

.1.70 

< ( <( 


which, when mixed loosely or spread in thin layers, will 
make about one and three-tenths yards bulk, and when 








WEIGHT OF EMBANKMENT MATERIALS. 


341 


thoroughly compacted in the embankment, will make about 
one and one-quarter cubic yards bulk. 

The voids now remaining in the mass may each be a 
thousand times broader than a molecule of water, yet they 
are sufficiently minute, so that molecular attraction exerts 
a strong force in each and resists flow of the molecules, 
even under considerable head pressure of water. 

It will be interesting here to compare the weights of a 
solid block of granite with its disintegrated products of 
gravel and sand, taking for illustration a cubic foot volume. 

TABLE No. 77. 

Weights of Embankment Materials. 


Material. 

Av. Weight. 

Specific Gravity. 

Av. Voids. 

Granite. 

166 

lbs. 

2.662 


Coarse Gravel. 

120 

<< 

I 9 2 5 

.28 per cent. 

Gravel. 

116 

u 

1.861 

.30 “ “ 

Sharp Sand. 

I IO 

it 

x - 7 6 5 

•33 “ “ 

Clay. 

I2 5 

a 

2.000 

.12 “ “ 

Water. 

62.5 

a 

1.000 

.... 


If the shingle is omitted and common gravel is the bulk 
to receive the flner materials, then the proportions in prac¬ 
tice may be: 

Common gravel. 1.00 cubic yard. 

Sand. 0.36 “ 

Clay. 0.25 “ “ 

1.61 

which, when loosely spread, will make about one and one- 
sixth yards bulk; and compacted, some less than one and 
one-tentli yards bulk. 

Gravel is usually found with portions of sand, or sand 
and clay, already mixed with it, though rarely with a suf- 





















342 RESERVOIR EMBANKMENTS AND CHAMBERS. 

ficiency of fine material to fill the voids. The lacking ma¬ 
terial should he supplied in its due proportion, whether it 
he fine gravel sand, fine sand, or clay. The voids must he 
filled, at all events, with some durable fine material, to 
ensure imperviousness. 

It is sometimes found expedient to substitute for a por¬ 
tion of the fine sand or clay, portions of loam or selected 
soil from old ground, and on rare occasions peat, hut 
neither peat nor loam should he introduced in hulk into 
the core of an embankment. 

There is a general prejudice against the use of peat or 
surface soils in embankments, and the objections hold good 
when they are exposed to atmospheric influences. Mr. 
Wiggin remarks,* however, that a peat sea-hank which was 
opened after being built for seventeen years, exhibited the 
material as fibrous and undecayed as when first deposited. 

Weight is a valuable property in embankment material, 
when placed upon a firm foundation, since, for a given bulk, 
the heavier material is able to resist the greater pressure. 

Peat and loam are very deficient in the weight property, 
and therefore need the support of heavier materials. Clay 
is heavier than sand or fine gravel; shingle is heavier than 
clay ; but the compound of shingle, gravel, sand, and clay, 
above described, is heavier than either alone, and weighs 
when compacted, for a given volume, nearly as much as 
solid granite. 

Cohesiveness and stability are valuable properties in 
embankment materials, but sand and gravel lack perma¬ 
nent cohesiveness, and clay alone, though quite cohesive, 
is liable to slips and dangerous fissures, if unsupported ; 
but a proper combination of gravel, sharp sand, and clay, 


* Embanking Lands from the Sea, p. 20. London, 1852. 




PECULIAR PRESSURES. 


343 


gives all the valuable properties of weight, cohesiveness, 
stability, and imperviousness. 

352. Peculiar Pressures. —There are peculiar pres¬ 
sure influences in an earthwork structure that are not 
identical with the theoretical hydrostatic pressures upon a 
tight masonry, or fully impervious structure of the same 
form. The hydrostatic pressure upon an impervious face, 
whatever its inclination, might be resolved into its hori¬ 
zontal resultant (§ 171), and that resultant would be the 
theoretical force tending to push the structure down the 
valley, and would be equal to the pressure of the same 
depth of water acting upon a vertical face. The pressure 
would be, upon a vertical face, per square foot , at the given 
depths, as follows: 


Depth, in feet. 

5 

IO 

15 

20 

25 

3 ° 

35 

40 

45 

50 

60 

70 

80 

1 

90 | IOO 

Pressure, in lbs. 

3 12 - 1 

624.3 

936-4 

1249 

1561 

1873 

2185 

2497 

2809 

3 121 

3746 

4370 

4994 

5618^6243 


The effective action of the theoretical horizontal resultant 
is neutralized somewhat upon an impervious slope by the 
weight of water upon the slope. 

But all embankments are pervious to some extent. If 
with the assistance of the pressure, the water penetrates to 
the centre of the embankment, it presses there in all direc¬ 
tions, upward, downward, forward and backward, and at a 
depth of fifty feet the pressure will be a ton and a half per 
square foot. Such pressure tends to lift the embankment, 
and to soften its substance, as well as to press it forward, 
and if in course of time the water penetrates past the centre 
it may reach a point where the weight or the imperviousness 
of the outside slope is not sufficient to resist the pressure, 
w T hen the embankment will crack open and be speedily 
breached. 

That portion of the embankment that is penetrated by 




















344 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


the water has its weight neutralized to the extent of the 
weight of the water, or at any depth, a total equal to the 
water pressure at that depth ; thus, at fifty feet depth, that 
portion penetrated is reduced in its total weight a total of 
one and one-half tons per square foot. 

Hence the value of imperviousness at the front as well 
as in the centre of the embankment, so that the maximum 
amount of its weight may be effective. 

If water penetrates the subsoil beneath the embankment, 
as is frequently the case, it there exerts a lifting pressure 
according to its depth. 

353. Earthwork Slopes.—If earth embankments of 
the forms usually given to them, and their subsoils also, 
were quite impervious, as a wall of good concrete would be, 
the embankments would have a large surplus of weight, 
and might be cut down vertically at the centre of their 
breadth, and either half would sustain the pressure and 
impact of waves with safety, but the vertical wall of earth 
would not stand against the erosive actions of the waves 
and storms. Surface slopes of earthwork are controlling 
elements in their design, and govern their transverse profiles. 

Different earths have different degrees of permanent 
stability or of f riction of their particles upon each other, 
that enable them to maintain their respective natural sur¬ 
face slopes, or angles of repose , against the effects of gravity, 
ordinary storms, and alternate freezings and thawings, until 
nature binds their surfaces together with the roots of weeds, 
grasses and shrubs. The coefficient of friction of earth 
equals the tangent of its angle of repose, or natural slope. 
The amount or value of the slope is usually described by 
stating the ratio of the horizontal base of the angle to its 
vertical height, which is the reciprocal of the tangent of the 
inclination. 


EARTHWORK SLOPES. 


345 


The following data relating to these values are selected* 
in part from Rankine, and to them are added the angles at 
which certain earths sustain by friction other materials laid 
upon their inclined surfaces. 


TABLE No. 78. 


Angles of Repose, and Friction of Embankment Materials. 


Material. 

Angle of 
Repose. 

Coefficient of 
Friction. 

Ratio 

of Slope. 

Diy sand, fine. 

28° 

•532 

Hori. 

1.88 

to 

Vert. 

I 

“ “ coarse.. . 

3 °° 

•577 

I *73 

u 

I 

Damp clay. 

45 ° 

1.000 

1.00 

u 

I 

Wet clay. 

15° 

.268 

3-73 

u 

I 

Clayey gravel. 

45 ° 

1.000 

1.00 

u 

I 

Shingle. 

42 

.900 

1.11 

u 

I 

Gravel. 

38 ° 

.781 

1.28 

u 

I 

Firm loam. 

36 ° 

.727 

i- 3 8 

u 

I 

Vegetable soil. 

35 ° 

.700 

1-43 

u 

I 

Peat. 

O 

20 

•364 

2-75 

u 

I 

Masonry, on clayey gravel.. 

3 °° 

•577 

i *73 

u 

I 

“ “ dry clay.. 

2 7 ° 

• 5 IQ 

1.96 

u 

I 

“ “ moist clay. .. 

i8° 

•325 

3.08 

u 

I 

Earth on moist clay. 

45 ° 

1.000 

1.00 

Ci 

I 

“ “ wet clay . 

i 7 ° 

.306 

3.26 

u 

I 


Inclined earth surfaces are most frequently dressed to 
the slopes, having ratios of bases to verticals, respectively 
1to 1 ; 2 to 1; 2 J to 1 ; and 3 to 1; corresponding respect¬ 
ively to the coefficients of friction 0.67, 0.50, 0.40, and 0.33, 
and to the angles of repose 33^°, 26J°, 21f°, and 18J°, 
nearly. 

Gravel, and mixtures of clay and gravel, will stand 
ordinarily, and resist ordinary storms at an angle of 1 \ to 1, 
but the angle must be reduced if the slope is exposed to 
accumulations of storm waters or to wave actions, and upon 


* Civil Engineering, p. 316. London, 1872. 

























346 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


broad lake shores the waves will reduce coarse gravel, if 
unprotected, to a slojoe of 5 to 1, and finer materials to 
lesser slopes. Complete saturation of clay, loam, and vege¬ 
table soil, destroys the considerable cohesion they have 
when merely moistened, and they become mud, and assume 
slopes nearly horizontal; hence the conditions to which the 
above table refers may be entirely destroyed and the angles 
be much flattened, unless the slopes are properly protected. 
On the other hand, the table does not refer to the temporary 
stability which some moist earths have in mass, for com¬ 
pact clay, gravel, and even coarse sand may, when their 
adhesion is at its maximum, or when their pores are par¬ 
tially and nearly filled with water, be trenched through, 
and the sides of the trench stand for a time, nearly vertical, 
at heights of from 6 to 15 feet. In such cases, loss or 
increase of moisture destroys the adhesion, and the sides of 
the trench soon begin to crumble or cave, unless supported. 

354. Reconnoissance for Site.—Let us assume, for 
illustration, that a storage reservoir is to be formed in an 
elevated valley. The minimum allowable altitude being 
fixed upon, and designated by reference to a permanent 
bench mark in the outfall of the valley, the valley is then 
explored from the given altitude upward for the most favor¬ 
able site for the storage basin, and for the site for an 
embankment, or dam, as the circumstances may require. 
We may expect to find a good site for the storage at some 
point where a broad meadow is flanked upon each side by 
abrupt slopes, and where those slopes draw near to each 
other at the outlet of the meadow, as is frequently the case. 
Having found a site that appears favorable, a preliminary 
reconnoissance with instruments is made to determine if the 
basin has the required amount of watershed and storage 
capacity, previously fixed upon (§ 59), and to determine 


DETAILED SURVEYS. 


347 


approximately the height the embankment or masonry 
dam must have. If the preliminary reconnoissance gives 
satisfactory results, then the site where the embankment 
can be built most economically and substantially is care¬ 
fully sought, and test pits and borings put down at the 
point giving most promise upon the surface. It is import¬ 
ant to know at the outset that the subsoil is firm enough to 
carry the weight of the embankment without yielding, and if 
there is an impervious substratum that will retain the pond¬ 
ed water under pressure. It is important also to know that 
suitable materials are obtainable in the immediate vicinity. 

355. Detailed Surveys. —The preliminary surveys all 
giving satisfactory indications as respects extent of flowage, 
volume of storage, depth of water, inclination and material 
of shore slopes, soils of flowed basin, and the detailed sur¬ 
veys confirming the first indications, and also establishing 
that the drainage area and rainfall supplying the basin is 
of ample extent and quantity to supply the required amount 

of water (§ 24) of suitable quality (§ 100 et seq .); then let 

* 

us suppose that the conditions governing the retaining em¬ 
bankment may best be met by a construction similar to 
that shown in Fig. 59, based upon actual practice. 

356. Illustrative Case.—Here the water was raised 
fifty feet above the thread of the valley. The surface of the 
impervious clay stratum, containing a small portion of fine 
gravel, was at its lowest dip, thirty feet below the surface 
of the valley, and was overlaid at this point, in the following 
order of superposition, with stratas of sandy clay, coarse 
sand, quicksand, sandy marl, gravel and sand, gravelly loam, 
and vegetable surface soil, each of thickness as figured. 

Gravel and sand and loam were obtainable readily in 
the immediate vicinity, but clay was not so readily pro¬ 
cured, and must therefore needs be economized. 


348 


RESERVOIR EMBANKMENTS AND CHAMBERS 


Fig. 59. 



STORAGE RESERVOIR EMBANKMENT. 

357. Cut-off Wall. —A broad trench, was cut, after the 
clearing of the surface soil, down to the sandy marl, and 
then a narrow trench cut down to eighteen inches depth in 
the thick clay strata, finishing four feet wide at the bottom. 

A wall of concrete, four feet thick, composed of machine- 
broken stone, four parts; coarse sand, one part; line sand, 
one part; and good hydraulic cement, one part, was built 
up to eighteen inches above the top of the marl stratum. 

The concrete was mixed with great care, and the materials 
rammed into the interstices of the bank, to insure imper¬ 
viousness in the wall, and to prevent water being forced 
down its side and under its bottom. Puddle, of one part 
mixed coarse and fine sharp gravel, one part fine sand, and 
one part good clay then filled the broad trench up to the 
surface of the embankment foundation. 

358. Embankment Core. —The core of the embank¬ 
ment was composed of carefully mixed coarse and fine 
gravel, sand, and clay, in the proportions given above 



















































































EMBANKMENT CORE. 


349 


(p. 340), requiring for one cubic yard of core in place, ap- 
proximately: 


Coarse gravel. 

Fine “ 


Sand. 


Clav. 


1.26 “ 


When measured by cart-loads, these quantities became 
eight loads* of mixed gravels, one load of sand, and two 
loads of clay, the cubic measure of each load of clay being 
slightly less than that of the dry materials. The gravel 
was spread in layers of two inches thickness, loose, the clay 
evenly spread upon the gravel and lumps broken, and the 
sand spread upon the clay. When the triple layer was 
spread, a harrow w T as passed over it until it was thoroughly 
mixed, and then it was thoroughly rolled with a two-ton 
grooved roller, made up in sections, the layer having been 
first moistened to just that consistency that would cause it 
to knead like dough under the roller, and become a com¬ 
pact solid mass. 

Such a core packs down as solid, resists the penetration 
or abrasion of water, nearly as well, and is nearly as diffi¬ 
cult to cut through as ordinary concrete, while rats and eels 
are unable to enter and tunnel it. 

The proportions adopted for the core was—a thickness 
of five feet at the top at a level three feet above high-water 
mark, and approximate slopes of 1 to 1 on each side. 

For the maximum height of fifty-four feet this gave a 
breadth of 113 feet base. 

This core was abundantly able to resist the percolation 
of the water through itself, and to resist the greatest pres- 

* Seven loads of coarse and three loads of fine gravel make, when mixed, 
about eight loads bulk. 









350 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


sure of the water, and had these been the only matters to 
provide for, the embankment core would have been the 
complete embankment. 

359. Frost Covering. —Frost would gradually pene¬ 
trate deeper and* deeper into that part of the work above 
water and into the outside slope, and by expansions make 
it porous and loose to a depth, at its given latitude, of from 
four to five feet. A frost covering was therefore placed 
upon it, and carried to a height on the inside of five feet 
above high-water line, and of just sufficient thickness at 
high-Avater line to protect it from frost. 

The frost-covering was composed of such materials as 
could be readily obtained in the vicinity of the embank¬ 
ment. It was built up at the same time, in thin layers, with 
the core, and the whole was moistened and rolled alike, 
making the whole so compact as to allow no apparent 
“ after settlement .” The wave slope was built eighteen 
inches full, and then dressed back to insure solidity be¬ 
neath the pavement. 

The core of an embankment should be built up at least 
to the highest flood level, which is dependent upon length 
of overfall as well as height of its crest, and the frost-cover¬ 
ing should be built of good materials to at least three feet 
above maximum flood level. 

3(>0. Slope Paving.— The exterior slope, when soiled, 
was dressed to an inclination of 1A to 1 ; the interior slope 
was made 2 to 1 from one foot above high water down to a 
level, three feet below proposed minimum low water, where 
there was a berm five feet wide, and the remainder of the 
slope to the bottom was made l\ to 1. The lower interior 
slope was paved with large cobbles driven tightly, the berm 
with a double layer of flat quarried stone, and the upper 
slope, which was to be exposed to wave action, was covered 


PUDDLE WALL. 


351 


with one foot thickness of machine-broken stone, like “ road 
metal," and then paved with split granite paving-blocks of 
dimensions as follows : Thickness, 10 to 14 inches ; widths, 
12, 14, or 16 inches ; and lengths, 24 to 48 inches. 

A granite ledge, in sheets favorable for the splitting of 
the above blocks, was near at hand, and supplied the most 
economical slope paving, when labor of placing and future 
maintenance was considered. From one foot above high 
water to the underside of the coping, the paving had a slope 
of 1 to 1, and the face of the coping was vertical. 

3G1. Puddle Wall. —The policy might be considered 
questionable of using clay in so large a section of the 
embankment, when the haulage of the clay was greater 
than of any of the other materials, and when the clay might 
be confined to the lesser section of the usual form of puddle 
wall. These methods of disposing the clay were compared 
in a preliminary calculation, both upon the given basis, and 
that of a puddle wall of minimum allowable dimensions, 
viz., five feet thick at the top and increasing in thickness 
on each side one foot in eight of height, which gave a maxi¬ 
mum thickness of 18.6 feet at base with 54 feet height. (See 
dotted lines in Fig. 59.) 

The estimate of loose materials for each cubic yard of 
complete core was—coarse gravel, .74 cu. yard ; fine gravel, 
.26 cu. yd. ; sand, .07 cu. yd. ; and clay, .15 cu. yd. ; and 
for puddle wall of equal parts of gravel and clay—gravel 
.59 cu. yd., and clay .59 cu. yd. 

This calculation gave the excess of clay in the maximum 
depth of embankment, less than 4 cubic yards per lineal 
foot of embankment, and the excess at the mean depth of 
thirty feet, about three-fourths yard per lineal foot of 
embankment. 

The difference in estimated first cost was slightly against 


f 



352 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


the mixed core, but in that particular case this was consid¬ 
ered to be decidedly overbalanced by more certainly in¬ 
sured stability, more probable freedom from slips and 
cracks in a vital part of the work, and by the additional 
safety with which the waste and draught pipes could be 
passed through the core. 

The value of puddle in competent hands has, however, 
been demonstrated in many noble embankments. It is 
usually placed in the centre of the embankment, as in 
Fig. 61, and occasionally near the slope pawng, as in 
Fig. 62, from a design by Moses Lane, C. E. 

3G2. Rubble Priming* Wall. — The drift formation 
presents a great variety of materials ; but not always such 
as are desired for a storage embankment, in the immediate 
vicinity of its site. The selection of proper materials often 
demands the best judgment and continued attention of the 
engineer. Clay, which is often considered indispensable in 
an embankment, may not be found within many miles. 

Fig. 60 (p. 84) gives a section of an embankment con¬ 
structed where the best materials were a sandy gravel and 
a moderate amount of loam, but abundance of gneiss rock 
and boulders were obtainable close at hand. 

Here a priming wall of thin split stone was carried up 
in the heart of the embankment from the bed-rock, which 
was reached by trenching. Each stone was first dashed 
clean with water, and then carefully floated to place in good 
cement mortar, and pains taken to fill the end and side 
joints, and exceeding care was taken not to move or in any 
way disturb a stone about which the mortar had begun to 
set, JSTo stones were allowed to be broken, spalted, or 
hammered upon the wall, neither were swing chains drawn 
out through the bed mortar. The construction of a water¬ 
tight wall of rubble-stone is a work of skill that can be 


APPLICATION OF FINE SAND. 


353 


performed, but the ordinary layer of foundation masonry 
in cement mortar seems no more to comprehend it than 
would a tiddler at a country dance the enchanting strains 
of a Vieuxtemps or Paganini. 

Grouting such rubble-stone walls, according to the usual 
method, will not accomplish the desired result, and is 
destructive of the most valuable properties of the cement. 

363. A Light Embankment. —In this embankment 
(Fig. 60), selected loam and gravel were mixed in due pro¬ 
portions on the upper side of the priming wall, so as to 
insure, as nearly as possible, imperviousness in the earth¬ 
work. The entire embankment was built up in layers, 
spread to not exceeding four or five inches thickness, and 
moistened and rolled with a heavy grooved roller. 

The cross-section of this work is much lighter than that 
advised by several standard authorities, both slopes being 
1 1 to 1, but great bulk was modified by the application of 
excellent and faithful workmanship. This embankment 
retains a storage lake of sixty-six acres and thirty feet 
maximum depth. It was completed in 1868, and has 
proved a perfect success in all respects. This work fills the 
offices of both an impounding and distributing reservoir, in 
a gravitation water supply to a New England city. 

364. Distribution Reservoirs. —Distributing reser¬ 
voirs are frequently located over porous sub-soils and 
require puddling over their entire bottoms and beneath 
considerable portions of their embankments, and puddle 
walls are usually carried up in the centres of their embank¬ 
ments or near their inner slopes. 

The same general principles are applicable to distrib¬ 
uting as to storage reservoir embankments. 

365. Application of Fine Sand. —Fig. 58 (p. 333) illus¬ 
trates a case where the bottom was puddled with clay, but a 


354 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


sufficiency of clay to puddle tlie embankments was not ob- 
tamable. The embankment is here constructed of gravel, 
coarse sand, very fine sand, and a moderate amount of 
loam. The materials were selected and mixed so as to 
secure imperviousness to the greatest possible extent, and 
were put together in the most compact manner possible, and 
have proved successful. This has demonstrated to the sat¬ 
isfaction of the writer that very fine sand may replace to a 
considerable extent the clay that is usually demanded, and 
his experience includes several examples, among which, on 
a single work, is more than tliree-fourths of a mile of suc¬ 
cessful embankment entirely destitute of clay, but sand 
was used with the gravel, of all grades, from microscopic 
grains to coarse mortar sand, and a sufficiency of loam was 
used to give the required adhesion. The outside slopes 
were heavily soiled and grassed as soon as possible. 


Fig. 61 . 



3GG. Masonry-faced Embankment. —When there 
is a necessity for economizing space, one or both sides of an 
embankment may be faced with masonry. 

An example of such construction is selected from the 
practice of a successful engineer in one of the Atlantic 







































EMBANKMENT SLUICES AND PIPES. 


355 


States, and is shown in Fig. 61. A method of introducing 
clay puddle into a central wall in the embankment, beneath 
the embankment, and on the reservoir bottom, is also here 
shown. The puddle of the reservoir bottom is usually 
covered with a layer of sand. 

.307. Concrete Paving. —The lower section of the 
slope paving of the distributing reservoir, Fig. 58, was built 
up of concrete, composed of broken stone 4 parts; coarse 
sand 1 part; tine sand 1 part; and hydraulic cement 1 part. 
The cement and sand were measured and mixed dry, then 
moistened, and then the stone added and the whole thor¬ 
oughly worked together. The concrete was then deposited 
and rammed in place, building up from the base to the top, 
in sections of about forty feet length. A very small quan¬ 
tity of water sufficed to give the concrete the proper con¬ 
sistency, and if more was added the concrete inclined to 
quake under the rammer, which was an indication of too 
much water. 

The general thickness of the concrete sheet is ten inches, 
and there is in addition four ribs upon the back side to give 
it bond with the embankment, and to give it stiffness, and 
also to check the liability of the sheet being lifted or cracked 
by back pressure from water in the embankment, when the 
water in the reservoir may be suddenly drawn down. 

The upper part of the slope that is exposed to frost is 
of granite blocks laid upon broken stone. The layer of 
broken stone at the wave line is fifteen inches thick, which 
is none too great a thickness to prevent the waves from 
sucking out earth and allowing the paving to settle. 

3G8. Embankment Sluices and Pipes.— Arched 
sluices have been in many cases built through the founda¬ 
tion of the embankment and the discharge pipes laid therein, 
and then a masonry stop-wall built around the pipes near 


356 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


tlie upper end of the sluice. By this plan the pipes are 
open for inspection from the outside of the embankment up 
to the stop wall. If the sluice is not circular or elliptical, 
its floor should be counter-arched, and its sides made strong, 
to resist the great pressure of the water that may saturate 
the earth foundation. 


Fig. 62. 



Such a sluice is sometimes built in a tunnel through the 
hillside at one end of the embankment. The latter plan, 
when the upper end of the tunnel is through rock, is the 
safer of the two, otherwise there is no place where it can be 
more safely founded, constructed, and puddled around, 
than when it is built upon the uncovered foundation of the 
embankment, either at the lowest point in, or upon, one 
side of the valley, since every facility is then offered for 
thorough work, which cannot so easily be attained in an 
earth tunnel obstructed by timber supports. 

A circular or rectangular well rising above the water 
surface, is usually built over the upper end of the sluice, 
and contains the valves of the discharge pipes, and inlet 
sluices at different heights, admitting water to the pipes 
from different points below the surface of the reservoir. 

When the sluice is used for a waste-sluice, also, the 
stop-wall is omitted, and the sluice well rises only to the 
weir crest level, or has openings at that level and an addi¬ 
tional opening at a lower level controlled by a valve. 















GATE CHAMBERS. 


357 


Sometimes heavy cast-iron pipes, for both delivery and 
waste purposes, are laid in the earthwork instead of in 
sluices, in which case the puddle should be rammed around 
them with thoroughness. In this latter case they should be 
tested, in place, under water pressure before being covered. 
A suitable hand force-pump may be used to give the 
requisite pressure if not otherwise obtainable. Bell and 
socket pipes with driven lead joints are used in such 
cases, and projecting flanges are cast around the pipes at 
intervals. 

The method of laying and protecting discharge pipes, as 
shown in Fig. 60 (p. 84), has been adopted by the writer in sev¬ 
eral instances with very satisfactory results. A foundation of 
masonry is built up from a firm earth stratum to receive the 
pipes, and then when the pipes have been laid and tested, 
they are covered with masonry or concrete. In such case 
the sides of the masonry are not faced, and pointed, or plas¬ 
tered, but the stones are purposely left projecting and 
recessed, and the covering stones are of unequal heights, 
making irregular surfaces. This method is more economi¬ 
cal in construction, and attains its object more successfully 
than the faced break-walls sometimes projected from the 
sides of gate-chambers and sluices. 

The puddle or core material is rammed against the ma¬ 
sonry in all cases, so as to fill all interstices solid. This 
portion of the work demands the utmost thoroughness and 
faithfulness; and with such, the structure will be so far 
reliable, and otherwise may be uncertain. 

369. Gate Chambers.— When an impounding reser¬ 
voir is deep, requiring a high embankment, it is advisable 
to place the effluent chamber upon one side of the valley 
toward the end of the embankment, with the effluent pipes 
for ordinary use only as low as may be necessary to draw 


358 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


the lake down to the assumed low water level, as in Fig. 63, 

showing the inside slope of an embankment. 

A waste-pipe for drawing off the lowest water is, in such 
case, extended from the front of the effluent chamber, side¬ 
ways down the slope and side of the valley to the bed of 
its old channel, and is fitted with all details necessary foi it 


Fig. 63. 



to perform the office of a siphon when there shall be occa¬ 
sion to draw the reservoir lower than the level of the gate 
chamber floor. By such arrangement the pipes may pass 
through the embankment, or through a sluice or tunnel in 
the side of a hill at a level twenty or twenty-five feet above 
the bed of the valley. 

When a valve-chamber is built up from the inner toe of 
the embankment, so that the water surrounds it at a higher 
level, provision must be made for the ice-thrust, lest it crowd 
back toward the embankment the upper portion sufficiently 
to make a crack in the wall; and precaution must also be 
taken to prevent the ice lifting bodily the whole top of the 














































































GATE CHAMBERS. 


359 


chamber when the water rises in winter, as it usually does 
in large storage reservoirs. 

The writer has usually connected the gate-house with 
the embankment by a solid pier, when there would other¬ 
wise be opportunity for the ice to yield behind the chamber 
by slipping up the paving, as it expanded, and thus en¬ 
danger the gate-chamber masonry. 

There are inlets through the front of the effluent chamber 
shown in Fig. 63, at different depths, permitting the water 
to be drawn at different levels. 

These, when the volume of water to be delivered is small, 
may be jrieces of flanged cast-iron pipe built into the 
masonry, with stop-valves bolted thereon, but usually are 
rectangular openings with cast-iron sluice - valves and 
frames (Fig. 64) secured at their inside ends. The seat and 
bearing of the valves are faced with a bronze composition, 
which is planed and scraped so as to make water-tight 
joints. The screw-stem of the valve is also of composition, 
or aluminum or manganese bronze. 

If such a valve exceeds 2-3" x 2-9" in area, or is 
under a pressure of more than twenty feet head, some form 
of geared motion is usually necessary to enable a single 
man to start it with ease. 

It is usually advisable to increase the number of valves 
rather than to make any one so large as to be unwieldy in 
the hands of a single attendant, even at the expense of some 
frictional head. 

The stem of the small valves usually passes up through 
a pedestal resting on the floor of the chamber, and through 
a nut in the centre of a hand-wheel that revolves upon the 
pedestal. 

The outside edge of each valve-frame should be so formed 
that a temporary wood stop-gate might be easily fitted 


360 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


Fig. 64. 


against it by a diver, in case accident required tlie removal 
of the valve for repairs. The chamber might then be readily 
emptied and the valve removed, without drawing down the 
lake. 

Upon the back of the valve (Fig. 64) are lugs faced with 
bronze, and upon the frame corresponding lugs, both being 
arranged as inclined planes, and their office is to confine the 
valve snug to its seat when closed. 

If the valve is secured to the side of the opening opposite 
to that which the current approaches, or to the pressure, its 

bolts must enter deep into or pass 
through the masonry. 

A slight flare is usually given to the 
sluice-jambs, from the sluice-frame out-, 
ward. 

370. Sluice-Valve Areas. —When 
the head is to be rigidly economized, 
3 the submerged sluice-valve area must 
be sufficient to pass the required vol¬ 
ume of water at a velocity not exceeding 
about five lineal feet per second; when 
the loss of head due to passage of the 
valve will not exceed about one-half 
foot. 

If Q is the maximum volume, in cu. 
ft. per second ; S, the area of the sluice 
in square feet; v, the assumed maxi¬ 
mum velocity; then 




Q = cSv, 


a) 


IRON SLUICE-VALVE. 


in which c is a coefficient of contraction, 
that may be taken, for a mean, as equal 
to .70 for ordinary chamber-sluices. 























































STOP-VALVE INDICATOR. 


361 


From tliis equation of Q, we derive that of area, 


cv 


( 2 ) 


Let Q = 70 cubic feet per second; v = 5 lineal feet 

per second ; then we have ^ = 20 square feet area, and we 

may make the valve opening, say 4' x 5'. 

If there are a number of valves, whose respective areas 
are s u s 2f s$... . s n , then 

Q 


cv 


- #1 + $2 d" $3 • • • • +S; 


nj 


( 3 ) 


Fig. 65. 


or advisedly we should give a slight excess to the sum of 

, Q 

areas and make + s 2 + s 3 . . . . + s n > —. 

C/ V 

371. Stop-Valve Indicator. —When a stop-valve is 
used, instead of a sluice-valve whose screw rises through 
the hand-wheel, it is usually desir¬ 
able to have some kind of an indi¬ 
cator to show how nearly the stop- 
valve is to full open. 

Fig. 65 illustrates such an indi¬ 
cator attached to the hand - wheel 
standard, as manufactured by the 
Ludlow Valve Co., at Troy, N. Y. 

A worm-screw upon the valve-stem 
revolves the indicator-wheel at the 
side of the standard, and indicates 
the various lifts of the valve between 

shut and full open. 

372. Power Required to Open 
a Valve. —The theoretical computa¬ 
tion of the power required to start a 
























































362 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


closed valve, when it is pressed to its seat by a head of water 
upon one side and subject only to atmospheric pressure on 
the other side, is attended with some uncertainties ; neverthe¬ 
less this computation, subject to such coefficients as experi¬ 
ence suggests, is a valuable aid when proportioning the parts 
of new designs. 

Take the case of the metal sluice-valve, Fig. 64, raised 
by a screw, with its nut placed between collars in the top 
of a pedestal, and revolved by a hand-wheel, and let the 
centre of water pressure upon the valve be at a depth of 
30 feet. Let the size of valve-opening be 2-6"x 2-9", the 
pitch of the screw .75 inch, and the diameter of the hand- 
wheel 30 inches. 

The weight has to slide along the spiral inclined plane 
of the screw, but its actual advance is in a vertical line, the 
pitch distance, for each revolution of the screw. 

The power is applied to the hand-wheel, which is equiva¬ 
lent to a lever of length equal to its radius, moving through 


a horizontal distance equal 
to the circumference of its 
circle (= radius x 6.283) 
and a vertical distance 


Fig. 66. 



| equal to the pitch of the 

screw. 

The distance d, moved through by the power in each 
revolution, is the hypothenuse be, Fig. 66, of an angle 
whose base, ab, equals the circumference of its circle, and 
whose perpendicular, ac, equals the pitch of the screw = 
^circumference 2 + pitch 2 = d. 

Let w be the weight in lbs.; p the pitch, in inches ; d the 
distance moved by the power per revolution, in inches, and 
P, the power, in foot-pounds.. 

According to a theory of mechanics, the 






POWER REQUIRED TO OPEN A VALVE. 


363 


Vel. of Power : Yel. of Weight :: Weight : Power; or, 
d : p :: w : P. 


The weight, in this case, includes the actual weight of 
the iron valve and its stem ; its friction upon its seat due to 
the pressure of water upon it; the friction of the screw upon 
its nut, and the friction of the nut upon its collar. These 
we compute as follows : 


Weight of valve, assumed 
Friction of valve (15469 lbs. pres, x coef. 20) 
Friction of screw (300 + 3094) x coef. 20 
Friction of nut (300 + 3094) x coef. 15 

Total equivalent weight, w 

Distance of power, d = jcircum. 2 x pitch 2 }! 
Pitch 

In the form of equation, 


= 300 lbs. 

= 3094 “ 

= 679 “ 

= 501 “ 

= 4574 “ 

== 94.25 inches. 
= .75 “ 


P = 


wp _ 4574 x .75 
d ~ 94.25 


= 36.4 lbs. 



Theoretically, this power applied at the circumference 
of the hand-wheel would be just upon the point of inducing 
motion, or if this power was in uniform motion around the 
screw, it would just maintain motion of the weight. The 
theory here admits that the screw and nut are cut truly to 
their incline, and that there is no binding between them due 
to mechanical imperfection. 

When two metal faces remain pressed together an ap¬ 
preciable length of time, the projections of each enter into 
the opposite recesses of the other, to a certain extent. These 
projections of the moving weight must be lifted out of lock, 
and the inertia of the weight must be overcome before it 
can proceed. Metal valves usually drop against an inclined 
wedge at their back that presses them to their seat, and 
there is also a fibre lock with this wedge, or “stick,” as it 






364 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


is commonly called, according to tlie force with which the 
valve is screwed home. 

Hence, the power required to start a valve is often double 
or treble, or even quadruple that that would theoretically 


be required to maintain it in motion the instant after start¬ 
ing. The equation for starting the valve in such case may 
become, 


4 wp _ p 

~1T ~ 



The computed distance which the power moves per revo¬ 
lution (94.25 inches) equals 7.854 feet, and the computed 
power 36.4 lbs. If twenty revolutions of the hand-wheel are 
made per minute, then the power exerted is theoretically 
7.854 ft. x 20 rev. x 36.4 lb. = 5717.7 foot-pounds per minute. 
This is a little more than one-sixtli of a theoretical horse¬ 
power. 

If, for the hand-wheel, which revolves the nut, there is 
substituted a spur-gear of equal pitch diameter, and into 
this meshes a pinion of one-tliird this diameter, and the 
same hand-wheel is placed upon the axle of the pinion, then 
the new power required will be reduced proportionally, as 
the square of diameter of the pinion is reduced from the 
square of diameter of the spur, or in this case, one-ninth. 

373. Adjustable Effluent Pipe. — An adjustable 
effluent pipe, capable of revolving in a vertical plane, and 
connected directly to the main supply pipe,* is shown in 
Fig. 60 (p. 84). 

This adjustable pipe is constructed of heavy sheet cop¬ 
per, and is sixteen inches in diameter. Upon its end is a 


* This ingenious form of flexible joint was suggested to the writer by Hon. 
Alba F. Smith, one of our most able American mechanical engineers. Mr. 
Smith designed this joint many years ago, and used it at watering stations 
upon the Hudson River, and other railroads under his charge. 





SLUICE VALVE. 



364 































































































































































































FISH SCREENS. 


365 


perforated bulb, through which the water enters the pipe. 
The movable section of the pipe is counter-weigh ted within 
the chamber, so the bulb can be set at any desired depth 
in the water, or raised out of water to the platform upon the 
chamber, for cleaning, expeditiously and easily by a single 
attendant. This arrangement has operated most satisfac¬ 
torily during the eight years since its completion, and de- 
livers the water supply for about 18,000 inhabitants. 

Equivalent devices have been adopted in several in¬ 
stances in Europe and in India, and they are especially 
applicable to cases where the impounding reservoirs are 
also the distributing reservoirs, without the intervention of 
filtering basins, and to cases where the surface fluctuates 
frequently, rapidly, or to a considerable extent. 

When a sudden or considerable decrease of the tem¬ 
perature of the air chills the quiet reservoir water surface, 
and thus induces a vertical motion in, or shifting of position 
of the whole mass of water, the bulb may be made to fol¬ 
low the most wholesome stratum. 

If the impounded water is to be led to filter-beds or to 
one or more distributing reservoirs, then the discharge- 
pipes lead directly from the effluent chamber. 

374. Fisli Screens. —In the chamber, Fig. 67, is shown 
a set of fish-screens, arranged in panels so as to slide out 
readily for cleaning. The finer ones of the double set are 
of No. 15 copper wire, six meshes to the inch, and the 
coarser ones of No. 12 copper wire, woven as closely as 
possible. 

Figs. 67 and 68 show a plan of and a vertical section 
through an influent chamber of a distributing reservoir. 

The pipes d d deliver water from the impounding reser¬ 
voir, or may be force mains, leading from pumping engines 
to the chamber A. The main chamber is divided in two 


366 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


Fig. 67. 



parts, for convenience in management when there are sev¬ 
eral delivery pipes. There are sluices Tc 7c, controlled by 
valves, through which the water may be admitted to the 
reservoir C. There is also a weir, i, over which water may 
be passed, instead of through the sluices. 


Fig. 68. 



10 5 0 10 20 30 3r0 

1 i i l t I I l i 1 1 i I|J_ l_I_I_I 

SECTION THROUGH INFLUENT CHAMBER. 


Grooves are prepared in each section of the main cham¬ 
ber for a double set of screens, ss. 



























































































































































































































GATE-CHAMBER FOUNDATIONS. 


367 


B is a waste chamber, and e a waste pipe, and w a w T aste 
overflow weir. 

A frost curtain, m , is placed in front of the inflow weir, 
to prevent the water surface in the chamber from freezing, 
if the pumps are not in operation during winter nights. 

There are drain pipes, y>, leading from the sections of 
the main chamber to the waste well. 

In the dividing partition is a sluice, with valve so that 
the whole chamber may be connected as occasion requires. 

A distributing reservoir effluent chamber might be simi¬ 
lar to the above, omitting the waste chamber, weirs, and 
frost curtain ; the direction of the current would in this case 
be reversed, of course. 

In the effluent chamber of the reservoir shown in Fig. 58, 
a check-valve is placed in the effluent pipe, so that when 
the pumps are forcing water into the distribution pipes 
around the reservoir, with direct pressure, the water will 
not return into the reservoir by the supply main. 

375. Gate-Cliamber Foundations.— Gate-chambers 
built into the inner slope of an earthwork embankment will 
introduce an element of weakness at that point, unless 
intelligent care is exercised to prevent it. 

Any after settlement along the sides of the foundation 
or walls of the chamber separates the earth from the 
masonry, leaving a void or loose materials along the side 
of the masonry, which permits the water of the reservoir to 
percolate along the side to the back of the chamber, under 
the full head pressure. 

The stratum of earth on which the foundation rests 
should be not only impervious, but so firm, or made so 
firm, that no settlement of the foundation can take place. 
If the chamber is high and heavy, the footing courses 
should be extended on each side so as to distribute the 


368 


RESERVOIR EMBANKMENTS AND CHAMBERS. 


weight on an area of earth larger than the section of the 
chamber. 

% 

The foundation of the chamber is to be water-tight, and 
capable of resisting successfully the upward pressure upon 
its bottom due to the head of water in the reservoir, when 
the chamber is empty. 

370. Foundation Concrete.— The use of beton , or 
hydraulic concrete, is often advisable for the bed-course of 
a valve-chamber foundation, to aid in distributing the 
weight of the structure and in securing a water-tight floor. 
The composition of the concrete is to be proportioned for 
these especial objects. Concrete for a revetment, demands 
weight as a special element; for a lintel, tensile strength; 
for an arch, compressile strength; but for the submerged 
foundation of a gate-chamber, imperviousness , which will 
ensure sufficient strength. 

The volume of cement should equal one and one-third 
times the volume of voids in the sand. The volume of mor- 

t 

tar should equal one and one-third times the volume of 
voids in the coarse gravel or broken stone. The cement 
and sand should be first thoroughly mixed, then tempered 
with the proper quantity of water equally worked in, and 
then the mortar should be thoroughly mixed with the 
coarse gravel or broken stone, which should be clean, and 
evenly moistened or sprinkled before the mortar is intro¬ 
duced. None of the inferior cement so often appearing in 
the market should be admitted in this class of work. Good 
hydraulic lime may in some cases be substituted for a 
small portion of the cement, say one-third. 

The concrete should be rammed in place, but never by 
a process that will disturb or move concrete previously 
rammed and partially set. A very moderate amount of 
water in the concrete suffices when it is to be rammed. 


CHAMBER WALLS. 


369 


377. Chamber Walls. — Fine-cut beds and builds, 
hammered end joints, and coursed work, in chamber ma¬ 
sonry, make expensive structures, but even such work is 
hardly made water-tight by a poor or careless mechanic. 
A great deal of skill and care must be brought into requi¬ 
sition to make a rubble wall water-tight. 

Imperviousness is here, again, a special object sought. 
That a wall may be impervious, its mortar must be imper¬ 
vious ; its voids must be compactly hlled, every one; its 
stones must be cleaned of dust, moistened, laid with close 
joints, and well bedded and bonded; and no stone must 
be shaken or disturbed in the least after the mortar has 
begun to set around it. 

Stone must not be broken or hammered upon the laid 
wall, or other stones will be loosened. Stones should be so 
lewised or swung that the bed or joint mortar shall not be 
disturbed when the stone is floated into place. 

The plan occasionally adopted of grouting several courses 
at the same time with thin liquid grout, might answer in a 
cellar wall wdien the object was to prevent rats from peram¬ 
bulating through its centre, but it is unreliable in a cham¬ 
ber or tank-wall intended to resist percolation under pres¬ 
sure. Skillful workmanship, in hydraulic masonry, is 
cheaper than expensive stock. 

24 




CHAPTER XVII. 


OPEN CANALS. - 

378. Canal Banks. —The stored waters of an impound¬ 
ing reservoir are sometimes conveyed in an open canal 
toward the distributing reservoir, or the city where they are 
to be consumed, or for the purposes of irrigation. The 
theory of flow in such cases has been already discussed 
(Chap. XY). 

The subsoils over which the canal leads require careful 
examination, and if they are at any point so open and 
porous as to conduct away water from the bed of the canal, 
the bed and sides must be lined with a layer of puddle 
protected from frost, as in Fig. 69, showing a section of a 
puddled channel in a side-hill cut. 


Fig. 69 . 



The retaining channel bank on the down-hill side is con¬ 
structed upon the same principles as a reservoir embank¬ 
ment (§ 351), the chief objects being to secure solidity, 
imperviousness, and permanence. 
























INCLINATIONS AND VELOCITIES. 


371 


A longitudinal drain along the upper slope of side-liill 
sections will prevent the washing of soil into the canal. 
The water slopes will require revetments or paving from 
three feet below low-water to two feet above high-water 
line, and paving or rubbling down the entire slope at their 


concave curves. 

Substantial revetments or pavings of sound stone are the 
most economical in the end. 

Revetments, built up of bundles of fascines laid with 
ends to the water and each layer in height falling back 
with the slope line, have been used to some extent on the 
banks of canals of transport, and on dykes.* 

If the slopes are rip-rapped, or pitched with loose stone, 
the slopes must be sufficiently flat, so the waves and the 
frost will not work the stones down into the water, and de¬ 
mand constant repairs. 

The retaining canal banks of the head races of water- 

powers have sometimes 
a longitudinal row of 
jointed-edged sheet-piles 
through their centre. The 
selected mixed earth is 
compactly settled on both 
sides of this piling, as 
shown in Fig. 70. Such 
piling tends to insure im¬ 
perviousness, prevent vermin from burrowing through the 
bank, and lasts a long time in compact earth. 

370. Inclinations and Velocities in Practice.— 
The unrevetted trapezoidal canals in earthwork, for water- 


Fig. 70. 



* Vide illustration of Foss Dyke in Stevenson’s Canal and River Engineer¬ 
ing, p. 18, Edinburgh, 1872; and Mississippi River Dyke at Sawyer’s Bend. 
Report Chief of U. S. Engineers, June 30, 1873. 






















372 


OPEN CANALS. 


supplies, irrigation, and for hydraulic power, except in 
water-powers of great magnitude, have sectional areas, 
respectively, between 500 and 50 square feet limits, and 
hydraulic mean radii between 7 and 2.5. 

In such canals the surface velocities range between 
5 feet and 2 feet per second, and the inclinations of surface 
between .75 feet (= .000104) and 3.5 feet (= .000663) per 
mile. 

Practice indicates that the favorite surface velocity of 
flow, iu such straight canals, is about 2.5 feet per second, 
in canals of about five feet depth, being less in shallower 
canals, and increased to 3.5 feet per second in canals of 
nine feet depth. 

Only very firm earths, if unprotected by paving or rub¬ 
ble, will bear greater velocities without such considerable 
erosions as to demand frequent repairs. 

Burnell states* that the inclinations given to the re¬ 
cently constructed irrigation canals in Piedmont and Lom¬ 
bardy, varies from -jgVo (= -000625) to (= .000278); 
but that inclinations frequently given to main conductors 
in the mountainous districts of the Alps, Tyrol, Savoy, 
Dauphine, and Pyrenees, is (= .002). 

380. Ice Coverings.—The maximum winter flow hav¬ 
ing been determined upon, the sectional area, beneath the 
thickest formation of ice at the lowest winter stage of water, 
must be made ample to deliver this maximum quantity of 
water, and the influence of the increase of friction on the ice 
perimeter over that on the equal air perimeter must be duly 
considered. 

381. Table of Dimensions of Supply Canals.— 

The dimensions and inclinations of a few well-known canals 


* Rudiments of Hydraulic Engineering, p. 127. London, 1858. 





CANAL GATES. 


373 


are given as illustrative of the general practice in various 
parts of the world, relating especially to mater supply and 
irrigation. 

TABLE No. 79. 

Dimensions of Water Supply and Irrigation Canals. 


Henares Canal, Spain. 

Roquefavour Canal, France... 
Marseilles “ “ 

Ourcq “ “ ... 

Montreal W. W. (old), Canada. 

“ “ (new), “ 

Manchester, N.H., W.W., U.S. 


Ganges Canal, India. 


Glasgow W. W., Scotland 


Cavour Canal, Italy- 


Form. 

Bottom 

Width. 

Side Slope. 

Depth, at 

Centre. 

Inclination. 

Ratio of 

Inclination. 

Mean 

Velocity. 

Trapezoidal. 

8.23 

I5 to I 

4.92 

1 in 3067 

.000326 

2.296 


9.84 

1) to 1 

4.92 

1 in 3333 

.OOO3 

.... 


9.84 

ig to 1 

5.58 

1 in 3000 

.000333 

2.72 


11.48 

i£ to 1 

4.92 

1 in 9470 

.0001056 

.... 


20 

Ij to X 

8 

1 in 25000 

.OOOO4 

...» 


78 

2 to 1 

14 

1 in 25000 

.OOOO4 

• • • • 


6 

1 to I 

14 

1 in 5280 

.000189 

.... 


150 

.... . . 

9 

. 

. ) 


and part 





. y 

3-7 

Twin Rect. 

85 


Q 




Rectangular. 

8 

. 

8 

1 in 6325 

1 

.000158 

1.478 

“ -1 

131 


6.1 

1 in 2800 

.000357 1 


i 

60 


11.15 

1 in 4000 

.00025 j 



Ill the numerous shallow irrigation canals of Spain, 
Italy, and northern India, a mean velocity as great as three 
feet per second is necessary to prevent a luxuriant growth 
of weeds on the bottoms and side slopes, which reduce the 
effective sectional area of the canal, and consequently the 
volume of water delivered. 

382. Canal Gates.—Fig. 71 is a half elevation of the 
gates in the Manchester, N. H., water-works canal, showing 
also a profile of the canal beyond the wing walls of the 
gate abutments. 

This canal leads the water from Lake Massabesic to the 
turbines and pumps at the pumping station. 

The water surface rises and falls with the lake, which 
has a maximum range of five feet, so that the turbines are 
constantly under the full head of the lake. The canal is 
sixteen hundred feet long, and has similar gates at its 






























374 


OPEN CANALS. 


i 


entrance and at the head of the turbine penstock. The 
entrance gates are provided with a set of iron racks to inter¬ 
cept floating matters that might approach from the lake, 
and the penstock gates are provided with a set of fine mesh 
copper-wire fish-screens. 

There are four gates in each set, each 3 feet wide and 
5 feet high. On the top of each gate is secured a cast-iron 


Fig. 71. 



tube containing a nut at its top. Over each tube is fastened, 
to a lintel, a composition screw, working in its nut, which 
raises or lowers its gate. 

Two gates in each set have their screws provided with 
gears and pinions. The pinions, or screws, are turned by a 
ratchet wrench, so the operator may turn them either way, 
to raise or lower the gate, by walking around the screw, or 
by a forward and backward motion of the arms. 

The floor covering the gate-chamber is of tar-concrete 
resting upon brick arches. 

















































































































MINERS’ CANALS. 


875 


When large sluices are necessary, a system of worm 
gearing is usually applied for hoisting and lowering the 
gates. These gears may be operated by hand-power, or 
may be driven by the belts or gears upon a counter-shaft, 
which is driven by a turbine or an engine. 

Canals leading from ponds subject to floods or sudden 
rise above normal level, are to be provided with waste-weirs 
near their head gates, and with waste-gates, so their banks 
will not be overtopped or their waters rise above the pre¬ 
determined height. 

Stop-gates are placed at intervals in long water-supply 
and irrigation canals, with waste-gates immediately above 
them for drawing off their waters, to permit repairs, or for 
flushing, if the waters deposit sediment. 

Culverts are sometimes required to pass the drainage of 
the upper adjoining lands beneath the canal, and these may 
be classed among the treacherous details that require ex¬ 
ceeding care in their construction to guard against settle¬ 
ments, and leakage of the canal about them. 

383. Miners’ Canals.—The sharp necessities of the 
gold-mining regions of California and Nevada have led to 
some of the most brilliant hydraulic achievements of the 
present generation. The miners intercept the torrents of 
the Sierras where occasion demands, and contour them in 
open canals, along the rugged slopes, hang them in flumes 
along the steep rock faces, syphon them across deep can¬ 
yons, and tunnel them through great ridges, in bold defi¬ 
ance of natural obstacles, though constant always to laws 
of gravity and equilibrium. 

The force of water is an indispensable auxiliary in sur¬ 
face mining, and capital hesitates not at thirty, fifty, or a 
hundred miles distance, or almost impassable routes, when 
the torrent’s power can be brought into requisition. A 


/ 


376 OPEN CANALS. 

hundred ditches , as the miners term them, now skirt the 
mountains, where hut a few years ago there was no evi¬ 
dence that the civilization or energy of man had ever been 
present. 

The Big Canyon Ditch, near North Bloomfield, Nevada, 
for instance, is forty miles long and delivers 54,000,000 
gallons of water per day. The sectional area of the stream 
is about 33 square feet, and the inclination 16 feet to the 
mile. Its flumes are 6 feet wide with grade of one-half 
inch in twelve feet, or about 18 feet to the mile. The con¬ 
tour line of the canal is from 200 to 270 feet above the 
diggings, to which its waters are led down in wrought- 
iron pipes. 

With a terrible power, fascinating to observe, its jets 
dash into the high banks of gravel, rapidly under-cutting 
their bases, and razing them in huge slides that flow down 
the sluice-boxes with the stream. 

Thus, in a single mine, 80,000 cubic, yards of gravel melt 
away in a single day, under the mighty hydraulic influence 
that has been gathered in the torrent and canaled along the 
eternal hills. 

The Eureka Ditch, in El Dorado County, is forty miles 
long, and there are many others of great length, whose 
magnitude and mechanical effect entitle them to considera¬ 
tion, as valuable hydraulic works, and monuments of 
hardy enterprise. 

The Eureka embankment is seventy feet in height, flows 
two hundred and ninety-six acres, and is located six thou¬ 
sand five hundred and sixty feet above the level of the sea. 


CHAPTER XVIII. 


WASTE-WEIRS. 

384. The Office and Influence of a Waste-Weir. 

-—An ample waste-weir is the safety-valve of a reservoir 
embankment. 

The outside slope of an earth embankment is its weakest 
part, and if a flood overtops the embankment and reaches 
the outer slope, it will be cut away like a bank of snow 
before a jet of steam. 

The overfall should be maintained always open and 
ready for use, independent of all waste sluices that are 
closed by valves to be opened mechanically, for a furious 
storm may rage at midnight, or a waterspout burst in the 
valley when the gate-keeper is asleep. 

Data relating to the maximum flood flow is to be dili¬ 
gently sought for in the valley, and the freshet marks 
along the watercourse to be studied. The overfall is to be 
proportioned, in both dimensions and strength, for the 
extraordinary freshets, which double the volume of ordi¬ 
nary floods, and if there are existing or there is a proba¬ 
bility of other reservoirs being built in the valley above, it 
may be wise to anticipate the event of their bursting, espe¬ 
cially if an existing reservoir dam is of doubtful stability. 

A short overfall may increase or affect the damage by 
flood flowage to an important extent, and makes necessary 
the building of the embankment to a considerable height 
above its crest level; while, on the other hand, a long over- 
fall, if exposed to the direct action of the wind, may permit 


378 


WASTE-WEIRS. 


too great a volume of water to be rolled over its crest in 
waves just at the commencement of a drought, when it is 
important to save, to the uttermost gallon. Such wave 
action, under strong winds, might draw down a small reser¬ 
voir several inches, or even a foot below its crest, unless 
such contingency is anticipated and guarded against. 
Strong winds blowing down a lake often heap up its waters 
materially at the outlet, and increase the volume of waste 
flowing over its weir or outfall. 

An injudicious use of flash-boards upon waste-weirs has 
in many instances led to disastrous results. In all cases, a 
maximum flood height of water should be determined upon, 
and then the weir dimensions be so proportioned that no 
contingency possible to provide for shall raise the water 
above the predetermined height. The length of the overfall 
and volume of maximum flood-flow govern the distance 
the highest crest-level must be placed below the maximum 
flood-level. Flash-boards may in certain cases, and in cer¬ 
tain seasons, be serviceable in governing the level of water 
below or just at the crest line , especially when there are low 
lands, or lands awash , as they are termed, bordering upon 
the reservoir, with their surfaces not exceeding three feet 
above the crest line. 

Several English writers mention that a general rule for 
length of waste-weir, accepted in English practice, is to 
make the waste-weir three feet long for every 100 acres of 
watershed. This rule will apply for watersheds not exceed¬ 
ing three square miles area, but for larger areas gives an 
inconvenient length. 

385. Discharges over Waste-Weirs. —Having de¬ 
termined, or assumed from the best data available, the 
maximum flood-flow which the overfall may have to dis¬ 
charge, if a very heavy storm takes place when the reservoir 


DISCHARGES OVER WASTE-WEIRS. 


379 


is fall, the overfall is then to he proportioned upon the 
basis of this flow. 

For the calculation of discharge, the overfall may be 
considered to be a species of measuring-weir (§ 303), and 
subject to certain weir formulas. 

If there are flash-boards, with square edges, forming the 
crest, then, for depths of from nine inches to three feet, Mr. 
Francis’ formula may be applied with approximate results, 
and we have the discharge : 

Q = 3.33 (Z - O.lnll) (1) 

in which Q is the volume of discharge, in cubic feet per 
second; II, the depth of water upon the crest, measured to 
the lake surface level; Z, the clear length of overfall; and 
n the number of end contractions. (Yide § 313, p. 289.) 

We have seen (§ 309) that the velocities of the parti¬ 
cles flowing over the crest are proportionate to the ordinates 
of a parabola, and that the mean velocity is equal to two- 
thirds the velocity of the lowest particles ; hence we have 
the mean velocity, v, of flow over the crest, 

v = lV2gB = 5.35 a/ IT. (2) 

Multiplying the depth of water II upon the weir, into 
the length Z of the weir, and into the mean velocity v, we 
have the volume of discharge, when there are no interme¬ 
diate flash-board posts: 

Q = mill x §a/2 glT= 5.35raZi7f, (3) 

in which m is a coefficient of contraction (§ 312), with 
mean value about .622 for sharp-edged thin crests. 

By transposition, we have : 

//= j-^ l • (4) 

( f ml V2(/\ 

If tlie overfall has a wide crest similar to that usually 
given to masonry dams, Fig. 47, then we may apply more 





380 


WASTE-WEIRS. 


accurately the formula suggested by Mr. Francis for such 
cases, viz.: 

Q = 3.012Z# 153 . (5) 

If we desire to know the depth of discharge for a given 
volume and weir length, then, by a transposition of this 
last formula, we have : 



A few approximate values of Q , for given values of H, 
are given in the following table, to facilitate preliminary 
calculations. Vide tables on pp. 290 and 298a. 

TABLE No. 80 . 

Waste-Weir Volumes per Lineal Foot for Given Depths. 


H. 

Q — 3.012///' 1,5 3 . 

Q=S. 3 SmlH*. 

In feet. 

In cu. ft. per sec. 

In cu. ft. per sec.* 

• 5 ° 

I.O43 

ImI 77 

•75 

I *939 

2.167 

1.00 

3. 012 

3-339 

1.25 

4.238 

4.670 

1.5° 

5.602 

6.134 

!-75 

7-°9 3 

7.625 

2. on 

8.699 

9-430 

2.2c; 

10.415 

11.244 

2.5® 

12.238 

I 3* I ^7 

2-75 

14.159 

I 5* I 93 

3. 00 

16.171 

I 7 - 3°9 

3 - 5 ° 


21.72 

4.00 


26.53 

4 - 5 ° 


3 I -66 

5.0° 


37.09 

5 - 5 ° 


46.91 

6.00 


48-75 

6.50 


54-97 

7.00 


61.43 

7 - 5 ° 


68.I3 

8.00 


75 .C 6 


* In this column m increases from .563 for 1 foot depth to .62 for 4 feet 
depth, but the values of m for depths exceeding 3 feet have not been de¬ 
termined by experiment, and their results are subject to some uncertainty. 

























REQUIRED LENGTH OF WASTE- WEIRS. 381 

386. Required Length of Waste-Weirs.—The fol¬ 
lowing table, prepared to facilitate preliminary calculations, 
gives estimated flood volumes of waste from small impound¬ 
ing reservoirs, in ordinary Atlantic slope basins, for water¬ 
sheds of given areas ; also the length of waste-weir required, 
and approximate depth of water on the crest of the given 
length : 

TABLE No. 81 . 

Lengths and Discharges of Waste-Weirs and Dams. 


A rea of Water¬ 
shed. 

Required length 
of overfall for 
given watershed. 

Approx, depth of 
water on overfall 
of given length. 

Approx, discharge 
per lin. ft. of given 
overfall, for given 
depth. 

Flood volume from 
whole area, 

Q — 200 ( M) j. 

Square miles. 

Feet. 

Feet. 

Cubic feet. 

Cubic feet per sec. 

1 I 

25 

I .89 

8 00 

200 

2 

32 

2 -35 

II .13 

356 

3 

39 

2.56 

12.82 

5 °° 

4 • 

44 

2.76 

14-43 

635 

6 

54 

2.91 

16.48 

890 

8 

61 

3.22 

18.54 

II3I 

IO 

68 

3-46 

20.04 

T 3 6 3 


83 

3-70 

23.01 

I9IO 

20 

95 

3 - 9 ° 

25-56 

2428 

2 5 

105 

4 - 1 3 

27.85 

2925 

3 o 

116 

4.28 

29-35 

3404 

40 

133 

4-58 

32-53 

4326 

5 ° 

149 

4.81 

34-95 

5208 

75 

183 

5 • 2 5 

39-92 

7304 

100 

212 

5-59 

43*78 

9282 

200 

2 95 

6 • 59 

56.08 

16542 

3 °° 

360 

7-23 

64.42 

2319O 

400 

400 

7 - 9 1 

73 - 7 ° 

29480 

5 °° 

440 

8.40 

80.68 

3550 ° 

600 

480 

8.77 

86.08 

41320 

800 

530 

9 • 63 

99.09 

52520 

1000 

58° 

10.27 

109.07 

63260 


The maximum flood, and consequently the required 
length of overfall, or depth upon it, varies with the maxi¬ 
mum periodic rainfall; the inclination and porosity of 














382 


WASTE-WEIRS. 


soils; the sum of pondage surfaces; and to some extent 
with temperatures. 

The above estimated flood volumes refer to ordinary 
American Atlantic slopes, and forty to fifty inch mean an¬ 
nual rainfalls, and to streams with comparatively small 
pondage areas. 

The above tabled lengths of overfalls or range of depths 
upon crests of waste-weirs, are to be increased for flashy 
streams, and may be reduced for steady streams with large 
or many small ponds. 

The increase of pressure upon all portions of the em¬ 
bankment and foundation, and upon the waste-weir, by the 
flood rise, must be fully anticipated in the original design 
of the structure. 

387. Forms of Waste-Weirs.—Fig. 72 illustrates a 
waste-weir placed in the centre of length of an earthwork 
embankment, retaining a storage lake of twenty-four hun¬ 
dred acres, and the drainage of forty square miles of water¬ 
shed. 

Fig. 72. 



The down-stream face of the weir is constructed in a 
series of steps of decreasing height and increasing projec¬ 
tion, from the crest downward, so that the edges of the steps 
nearly touch an inverted parabolic curve. 

































































ISOLATED WEIRS. 


383 


The apron receiving the fall of waste water from the 
crest of the weir is of rubble masonry, and contains two 
upright courses intended to check any scour from the 
“undertoe” during freshets, and also to lock the founda¬ 
tion courses that receive the heaviest shocks of the falling 
water. 

The projection of the steps was arranged to break up 
the force of the falling water as much as possible. 

The fall from crest to apron is twenty-five feet, and the 
flood depth upon the weir twenty inches ; yet the force of 
the falling water is so thoroughly destroyed that it has not 
been sufficient to remove, in three years service, the coarser 
stones of some gravel carted upon the apron during con¬ 
struction of the upper courses of the weir. 

There is a 3 by 5 feet waste-sluice through the weir at 
one end, discharging upon the apron. In front of the sluice 
the apron consists of two eighteen-inch courses of jointed 
granite upon a rubble foundation, doweled and clamped 
together in a thorough manner. 

A carriage-bridge spans the weir, and rests upon the 

r 

wing walls and three intermediate piers built upon the weir. 

388. Isolated Weirs. —Where the topography of the 
valley admits of the waste-weir being separated from the 
embankment, it should be so placed at a distance, and it 
is often conveniently made to discharge into a side valley 
where the flowage nearly, or quite, reaches a depression in 
the dividing ridge. 

But it is not always admissible to so divert the water, as 
riparian rights may be affected, or flood damages be created 
on the side stream. 

When possible, it is advisable to locate the waste-weir 
upon a ledge at one end of the embankment, so that the 
fall from the crest will not exceed three or four feet. 


384 


WASTE-WEIRS. 


There should be a fall of at least three feet from the crest, 
as in such case a less length of weir will be required than if 
it slopes gently away as a channel. 


Fig. 73. 



389. Timber Weirs.—In those localities where sound 
and durable building-stones are scarce, and timber is plenty 
and cheap, the waste-weir may be substantially constructed 
of timber in crib form. Fig. 73 represents such a weir 
placed upon a gravel foundation. The fall is twenty feet, 
and the face of the weir is divided into three benches so as 
to neutralize the force of the fall that in freshets, if vertical, 
i would tend to excavate a hole in the gravel in front of the 
dam at least two-thirds as deep below the lower water sur¬ 
face as the height of the fall. 

The timbers are faced upon two sides to.twelve inches 
thickness and entirely divested of bark. The bed-sills are 












































TIMBER WEIRS. 


385 


sunk in trenches in the firm earth, and two rows of jointed 
sheet-piling are sunk, as shown, to a depth that will prevent 
the possibility of water working under them. Upon the 
bed-sills longitudinal timbers are laid five feet apart, then 
cross timbers as shown, and so alternately to the top. As 
each tier is put upon another it is thoroughly fastened to 
the lower tier by trenails or f-inch round iron bolts. The 
bolts should pass entirely through two timbers depth and 
one-half the depth of the next tier, requiring for twelve-inch 
timbers 30-incli bolts. 

As each tier is laid it should be filled with stone ballast 
and sufficient coarse and fine gravel puddled in to make the 
work solid, leaving no interstices by the side of or under 
timbers. The gravel should be rammed under the timbers 
so as to give them all a solid bearing. 

A tier of plank is placed under each bench capping, and 
a tier of close-laid timbers is placed under the crest capping. 
The bench and crest cappings are of timbers jointed upon 
their sides and laid close. The upper and lower faces are 
planked tight with jointed plank. 

A weir thus solidly and tightly constructed will prove 
nearly as durable as the best masonry structures. The 
capping and face plankings will be the only parts requiring 
renewal, and these only at intervals of a number of years 
if they are at first of proper thickness. 

Similar forms of crib-work have been used with com¬ 
plete success on rock bottoms, on impetuous mountain 
streams, where they were subject to the shocks of ice at the 
breaking up of winter, and to great runs of logs in the 
spring. In such cases the bed-sills are bolted to the rocks. 

Similar crib foundations may be used to carry masonry 
weirs upon gravel bottoms, but the crib-work should in 
such case be placed so low as to be always submerged. 

25 


386 


WASTE-WEIRS. 


Fig. 73 was designed for a case where the watershed is 
of about one hundred square miles area. Its crest-length is 
two hundred feet, and six feet is the estimated maximum 
flood-depth upon its crest. 

390. Ice-thrust upon Storage Reservoir Weirs.— 

Those weirs that are located in Northern climates upon 
storage ponds, such as are drawn down in summer and do 
not rise to the crest-level until past mid-winter, should be 
backed with gravel to the level of the backs of their caps, 
and the gravel should be substantially paved, as in Fig. 72. 
Otherwise the expansion of the thick ice against the verti¬ 
cal backs of the weirs may act with such powerful thrust as 
to displace or seriously injure its upper portion. 

391. Breadth of Weir-Caps .—The cap-stones of weirs 
in running streams should incline downward toward the 
pond side at least two inches for each foot of breadth, so 
that the floating ice and logs will not strike against their 
back ends when the water is flowing rapidly. 

There is a lack of uniformity, in practice, in breadths of 
tops of waste-weirs, and the unsatisfactory working of the 
quarry from which the caps are supplied often controls 
this dimension so far as to reduce it to an unsubstantial 
measure. 

The breadth of cap required depends somewhat on the 
pond behind the weir. If the pond is relatively broad and 
deep, water and whatever floating debris it carries, will 
approach the weir with a relatively low velocity. If the 
pond is small and the stream torrential, with liability of 
great depth upon the weir, then the cap-stones must have 
length and weight to resist the force of the current and im¬ 
pact of the floating bodies. Overfalls upon logging streams 
rising in the lumber regions, require particularly heavy 
caps, and the force of the logs or ice upon the caps will 


THICKNESS OF WASTE-WEIRS AND DAMS. 


387 


usually be greater wlien tlie depth upon the weir is from 
one and one-half to two feet, than when deeper. 

892. Thickness of Waste-Weirs and Dams.—If 
the back, or pond side of the dam, is vertical, and the thick¬ 
ness at cap constant, then the thicknesses at given depths 
may be found, for plotting a trial section, by the following 
equation: 

Let b be the assumed top breadth, and t the thickness 
at any given depth, d> then 

t - b + .ldK (7) 

For illustration, let the assumed cap breadth, or length 
of cap stones, for a long straight dam, be eight feet, then 
for the following given depths, the ordinates or thicknesses 
are as follows: 


TABLE No. 82 . 

Thickness for Masonry Weirs and Dams. 


Depths from top 

OF CAP. 


Thickness. 

Feet. 

(A) 


(.1 d\.) 


Feet. 

O 

8 

4 - 

O . O 

- 

8.00 

4 

8 

+ 

.8 

— 

8.80 

6 

8 

4 - 

1.47 

— 

9-47 

8 

8 

+ 

2.26 

— 

10.26 

IO 

8 

+ 

3.16 

— 

11.16 

12 

8 

+ 

4.16 

— 

12.16 

15 

8 

+ 

5 - Sl 


x 3 • 8r 

20 

8 

4 - 

8.94 

— 

16.94 

2 5 

8 

4 - 

12.50 

— 

20.50 

30 

8 

4 - 

16.43 

== 

24-43 

35 

8 

4 - 

20.71 

— 

28.71 

40 

8 

4 " 

2 5 - 3 o 

— 

33-30 

45 

8 

4 - 

3°- I 9 

— 

3 8 l 9 

5 ° 

8 

_u 

1 

35-36 

— 

43 - 3 6 


If the face curve is resolved into an ogee or into steps, as 
is advisable over gravel bottoms or tertiary rock, then the 










388 


WASTE-WEIRS. 


masonry of the lower curve and steps must be very heavy 
and substantial, in the high dams, to withstand for a long 
term of years the shock of the falling water. 

393. Force of the Overflowing* Water. —It is of 
the utmost importance that the water passing over the lip 
of a high dam shall reach the bed of the stream below the 
dam with the least possible shock to the foundation, even 
though it is of a tolerably hard rock, and especially if the 
apron be of concrete or crib-work. 

The “life” of numerous upright-face dams has been 
materially shortened by the tremor due to the flood falls 
upon their foundations. 

In the case of an overfall twenty-five feet high, with six 
feet depth of water above the crest, for instance, there is a 
force of nearly 80,000 pounds per second pounding upon 
each lineal foot of its apron, tending to shake the structure 
into granular disintegration, and making the earth tremble 
under the shock. 

394. Heights of Waves. — Stevenson gives, in his 
treatise on Harbors, the following formula for computing 
the height of waves coming from a given exposure, or 
“fetch” of clear deep water: 

77 = 1.5 VI) + (2.5 - v'S), (8) 

in which 77 is the height of waves in feet, and D is the length 
of exposure or fetch in miles. 

The numerical values of height of wave, according to 
this formula, for given exposures, are as follows: 


TABLE No. 83. 


Heights of Reservoir and Lake Waves. 


Exposure, in miles. 

Height of wave, in feet.. 


•25 

•50 ! -75 

i 

i-5 

2 3 

5 

10 . 

2-543 

2 . 756 . 2.868 

3 

3-031 

3 . 33213-782 

4.437 

5 . 466 . 













HEIGHTS OF WAVES. 


389 


When waves meet a paved slope their vertical longi¬ 
tudinal section is suddenly reduced and their velocity en¬ 
hanced in inverse proportion. They will therefore rise up 
the slope to a vertical height much greater than the height 
of the approaching wave, which height will depend on both 
the initial velocity of the wave and the suddenness with 
which its sectional area is reduced, -s 


CHAPTER XIX. 

PARTITIONS, AND RETAINING WALLS. 

305. Design. —The hydraulic engineer finds necessary 
exercise for his skill on every hand to adapt a variety of 
constructions in masonry to their several ends, in methods 
at once substantial and economical. 

Designs are required for reservoir partitions and gate 
chambers that are to sustain pressures of water upon both 
sides, and either side alone; revetments for reservoirs, 
canals, and lake and river fronts that are to sustain pres¬ 
sures of water and earth upon opposite sides, and earth 
alone upon one side; coal-shed walls that are to sustain 
the pressure of coal, whose horizontal thrust nearly equals 
that of a liquid of equal specific gravity ; conduit and filter 
gallery walls, that are to sustain pressures of earth and 
water and thrusts of loaded arches; basement walls and 
bridge abutments that are to sustain thrusts of earth and 
carry weight; wing walls of triangular elevations and vary¬ 
ing heights, that are to sustain varying thrusts ; and waste- 
weirs, that are to sustain pressures of water higher than 
their summits and moving with velocity. 

Rule of thumb practice in such structures has led to 
many failures, when the amounts and directions of thrusts 
w T ere not understood ; and such failures have, on the other 
hand, led to the piling up of superfluous quantities of 
masonry, often in those parts of section where it did not 
increase the stability of position, but did endanger the 
stability of the foundations. 






DAM ON NATCHAUG RIVER, WILLIMANTIC, CONN. To face P . 391 . 

r 

(The arrow gives position of the resultant when there is six feet depth of flood on the overfall.) 






















































































































































































































































































































































































































THEORY OF WATER PRESSURE. 


391 


Good design only, unites economy witli stability in 
masonry subjected to lateral thrusts. 

396. Theory of Water Pressure upon a Vertical 
Surface. —The theory of pressure of water upon a plane 
surface, and of the stability of a vertical rectangular retain¬ 
ing wall, is quite simple, and is easily exemplified by 
graphic illustration, and by simple algebraic equations. 

Let BD, Fig. 74, be a vertical plane, receiving the 
pressure of water. 

The pressure, p, at any depth is proportional to that 
depth into the density of the fluid. 

Let w x be the weight of one cubic foot of water = 
62.5 lbs. ; then the pressure upon any square foot of the 
vertical plane, whose depth of centre of gravity is represent¬ 
ed by d , is p = dw x . 

Let the depth of the water B 2 D be 12 feet = 7^. Plot in 
horizontal lines from B 2 D, at several given depths, the 
magnitudes of the pressures at those depths =dw x , as at ss x ; 
then the extremities of those lines will lie in a straight line 
passing through B , and cutting the horizontal line CD/, in 
f, Df being equal to the magnitude of the pressure at D. 

The total pressure upon the plane B 2 D , and its horizon¬ 
tal effects at all depths are graphically represented by the 
area and ordinates of the figure B,f D. 

In theoretical statics, the effect of a pressure upon a 
solid body is treated as a force acting through the centre of 
gravity of the body. 

Consider the pressure of B,fD to be gathered into its 
resultant , passing through its centre of gravity,"- g. The 


* To find tlie centre of gravity of a triangle BfD, draw a broken line from 
J), bisecting tlie opposite side in s,, and from/, bisecting tlie opposite side in 
s : the centre of gravity will then lie in the intersection of those lines. Or 
draw a line from any angle B 2 , bisecting the opposite side, and the centre of 





392 


PARTITIONS, AND RETAINING WALLS. 


Fig. 74. 



horizontal resultant through g will meet B 2 D in iV 7 , at two- 
thirds the depth B 2 B. 

Let JDCB he a section of wall one foot long. Let B 2 D 


gravity will lie in this line, at one-tliird the height from the side bisected. 
The centre of gravity is at two-tliirds the vertical depth B 2 D = §h from B.,. 


12 FEET 
































































WATER PRESSURE UPON AN INCLINED SURFACE. 393 


= h — 12 ft. The centre of gravity of the submerged wall 

surface B,D is at one-half its height, = The total 

pressure of water P upon the wall-surface B 2 D equals the 
product of the surface area , B 2 D — A h into the weight of 
one cubic foot of water, into one-lialf the height, = 

7) 7) 2 

P= — =w x — ( 1 ) 

19 

= (12 x 1) x 62.5 x ~ 

£ 

= 4500 pounds = 2.25 tons. 


Draw this total pressure to scale, in the resultant gN, 
meeting B 2 D in N. 

The effect of a pressure, when applied to a solid body, 
is the same at whatever point in the line of its direction it 
is applied; so we may consider gN as acting upon the wall 
either at N or at x, in the vertical through the centre of 
gravity of the wall. 

The force tending to push the wall along horizontally 
is gN. 

397. Water Pressure upon an Inclined Surface. 

—The maximum resultant of pressure of water upon the 
inclined plane JC has a direction perpendicular to the 
plane, and meets the plane in P l5 at two-thirds the vertical 
depth of the water. 

The entire weight of the triangular body of water CiJ is 
supported by the masonry surface JC. Its vertical pressure 
resultant upon JC passes through its centre of gravity in g z , 
and meets JC in P 1? at two-thirds the vertical depth iC or 
JC. Its horizontal pressure resultant also meets JC in P 1o 

Let X\ be the symbol of its horizontal resultant. 

“ e “ “ “ vertical “ 


u 


u 


y 


u 


ii 


u 


maximum 


394 


PARTITIONS, AND RETAINING WALLS. 


The horizontal effect of the pressure, x x , may be com¬ 
puted as acting upon the plane of its vertical projection or 
trace, iC, and will equal, 

Xi = A^Wi ~ ■ OTi, (2) 

= 2.25 tons, when 7^ = 12 ft. 


Draw x x = 2.25 tons to scale in x x P x . Let fall a perpen¬ 
dicular upon JC, meeting it in P x ; then will the angle 
yP x x x equal the angle JCi — 0, and y7^will equal * 


y — x x - sec 0 = | \ | * sec ail gl e X \P\V (3) 

= 2.714 tons; 


and eP x will equal 

e 

— 1.518 tons. 


( 7i 2 ) 

= X\ • tan 0 = -j Wy — j- • tan angle x x P x y 



The horizontal force tends to displace the wall horizon¬ 
tally. The vertical downward force tends to hold the wall 
in place, by friction due to its equivalent weight. 

If water penetrates under the base of the wall, it will 
there exert an upward pressure upon the base, opposed to 
the downward pressure upon JC, and to the weight of the 
wall, with maximum theoretical effect equal to area CD 
into depth of its centre of gravity into the weight of one 
cubical foot of water. 

Let z x he the symbol of the maximum upward pressure, 
and let c x be the ratio of the effective upward pressure in 
any case to the maximum. 

Draw CyZy in the vertical line through the centre of gravity 
of the masonry, in Gz x . 

When computing the resultant weight of the masonry, 


* Vide trigonometrical diagram and table in tlie Appendix. 




FRICTIONAL STABILITY OF MASONRY. 


395 


opposed to the horizontal water pressure, deduct from the 
weight ot wall the excess of upward, c x z, over downward 
pressure, e, = c^z — e. 

398. Frictional Stability of Masonry.— The weight, 
W, in pounds, of the wall (of one foot length) equals its 
sectional area DOB = A, in square feet, into the weight of 
one cubical foot 10 of its material: W = Aw. (5) 

The downward resultant of weight is 

W r = {Aw) + e — (CiZi). (6) 

The upward pressure of the water upon the base will rare¬ 
ly exceed 50 per cent, of the theoretical maximum, even 
though the wall is founded upon a coarse porous gravel, or 
upon rip-rap, without a like upward relief of backfilling. 

The frictional stability , S, of the wall, equals its result¬ 
ant weight into its coefficient, c, of friction, 

S = { IF + e — {c^i)\ x c. (7) 

Foundations of masonry upon earth are usually placed 
in a trench, by which means the frictional stability upon 
the foundation is aided by the resistance of the earth side 
of the trench, and the coefficient thus made at least equal to 
unity. In such case the measure of resistance to horizontal 
displacement is the friction of some horizontal or inclined 
joint. 

The value of the adhesion of the mortar in bed-joints is 
usually neglected in computations of horizontal stability, 
and sufficient frictional stability should in all cases be given 
by weight, so that the resistance of the mortar may be 
neglected in the theoretical investigation. 

If, however, the mortar is worthless, or its adhesion is 


* Submerged unmortared masonry and porous back-filling are reduced in 
effective weight an amount equal to the weight of the water actually displaced. 




396 


PARTITIONS AND RETAINING WALLS. 


destroyed by frost or careless workmanship, or otherwise, 

then the mortar becomes equivalent to a layer of sand as a 

lubricant, and the coefficient of friction may thus be reduced 

verv low. 

«/ 

399. Coefficients of Masonry Friction.— The fol¬ 
lowing table of coefficients of masonry frictions will be found 
useful.* They are selected from several authorities, and 
have been generally accepted as mean values. 

TABLE No. 84. 

Coefficients of Masonry Frictions (Dry). 




» 


Coef. 

Angle 

of 

Repose 

Point dressed granite 

(medium) 

on 

dry clay. 

• 5 i 

O / 

27.0 

it a a 

it 

ii 

moist clay. 

•33 

18.15 

ii ii it 

ft 

ii 

gravel. 

•58 

30 

it a n 

« , 

it 

like granite. 

.70 

35 

it a u 

ii 

ii 

common brickwork. 

•63 

32.2 

a a a 

ii 

ii 

smooth concrete. 

.62 

31.48 

Fine cut granite 

ii 

ii 

like granite. 

•58 

30 

Very fine cut granite 


ti 

ii ti 

.61 

30.30 

it ii it 


ii 

pressed Beton Coignet... 

.61 

30.30 

Dressed hard limestone (medium) 

ii 

like limestone. 

•38 

20.48 

ii ii ii 

ii 

ti 

brickwork. 

.60 

3 1 

Beton blocks 

(pressed) 

ti 

like Beton blocks. 

.66 

33-15 

Polished marble 

it 

common bricks. 

.44 

23-45 

ii ii 


i t 

fine cut granite. 

.61 

30.30 

Common bricks 


it 

common bricks. 

.64 

32.38 

ii ii 


it 

dressed hard limestone... 

.60 

3 i 


When S and are equal to each other, the wall is just 
upon the point of motion, and S must be increased; that 
is, more weight must be given to the wall to ensure frictional 
stability. 

Let the water be withdrawn from the side BD, Fig. 74, 
and let the upward pressure attain to one-lialf the maxi¬ 
mum, and the coefficient be that of a horizontal bed-joint 
upon a concrete foundation, assumed to be .62, then S = 


\ 


* Vide § 353 , pp. 344 , 345 . 




























LEVERAGE STABILITY OF MASONRY. 


397 


(TF+ e — .502,) x c = 2.79 tons, and x Y — 2.25 tons, and the 
wall has a a small margin of frictional stability. 

The weight of the wall should be increased until it is 
able to resist a horizontal thrust of at least 1.5#,, or until 
S = 1.5^i, when the equation of frictional stability becomes 

S = (TF+ e — C&) x c = 1.5x h (8) 

in which 

TV is the weight of masonry above any given plane. 

e “ vertical downward water pressure resultant. 

Z\ u maximum upward water pressure resultant. 

Ci “ ratio of effective upward water pressure to the 
maximum. 

c “ coefficient of friction of the given section upon 
its bed. 

x x u horizontal water pressure resultant. 

S “ symbol of frictional stability. 

400. Pressure Leverage of Water.—Since the hori¬ 
zontal resultant of the water-pressure has its point of appli¬ 
cation above the level of Z>, in iV, its moment of pressure 
leverage , L , has a magnitude equal to DJV, or Kx = 
into the horizontal resultant. 

r A 7i 7i 7i 3 

L - AyWi j x -g,= -g- w x . (9) 

401. Leverage Stability of Masonry.—The moment 
of pressure-leverage of the water tends to overturn the wall 
about its toe, D or (7, Fig. 74, opposite to the side receiving 
the pressure alone, or the maximum pressure. 

Let the weight of DCB , per cubical foot, be assumed 
140 pounds, an approximate weight for a mortared rubble 
wall of gneiss, or mica-slate; then the total weight above 
the bed-joint CD , is 140 A = 5.25 tons, which we may con- 


398 


PARTITIONS, AND RETAINING WALLS. 


sider as acting vertically downward through G , the centre 
of gravity of DCB. 

Plot to scale this vertical resultant of weight in xe 2 = 
5.25 tons (neglecting for the present the upward and down¬ 
ward pressures of the water), and the horizontal resultant 
of water pressure in xN 2 = 2.25 tons, and complete the 
parallelogram xN 2 Me 2 ; then the diagonal xM, is in mag¬ 
nitude and direction the final resultant of the two forces. 
The resultant arising from the horizontal pressure on 
JC\ and weight of the masonry, is in magnitude and direc¬ 
tion xO. 

If the directions of xM and xO cut the base DC, then the 
wall has, theoretically, leverage stability, but if the direc¬ 
tions of these diagonals are outside of DC, then the wall- 
lacks leverage stability and will be overturned. 

For safety, the direction of xM should cut the base at a 
distance from K not exceeding one-half KC, and the direc¬ 
tion of xO cut the base at a distance from K not exceeding 
one-half KD. 

402. Moment of Weight Leverage of Masonry.— 

Since the vertical resultant of weight of masonry takes its 
direction through G, and cuts DC at a distance from C, 
the point or fulcrum over or around which the weight must 
revolve, the moment of weight leverage of the wall has a 
magnitude, when resisting revolution to the right, equal to 
the distance KD into the vertical weight resultant; and 
when resisting revolution to the left, equal to the distance 
KC into the vertical weight resultant.. 

Let the symbol of distance of K from the fulcrum, on 
either side, be d u and its value be computed or taken by 
scale, at will; and let the symbol of moment of weight 
leverage be M, then 


M = Awdi. 


(10) 


MOMENTS OF SECTIONS. 


399 


For double stability, or a coefficient of safety equal to 2, 

—must, at least, be equal to or 

Z 6 

li 3 

M= ~w x . 

O 

403. Thickness of a Vertical Rectangular Wall 
for Water Pressure. 

Let li be the height of the wall and of the water. 

“ w “ weight of a cubic foot of the masonry. 

“ water. 


“ w x “ 


u 


u 


u 


“ z “ required thickness of the wall. 

2 , 

Then li x z x — x w = leverage moment of weight of 

£ 

wall, = ; and h x ^ x w x x \ = leverage moment of 

Z Z o 


pressure of water = for double effect, 


h z w 1 


The equation for a vertical rectangular wall, Fig. 75, 
that is to sustain quiet water level with its top, and that 
just balances a double effect of the water is: 

hz'w _ ~h z w x 

"IT - ~1T’ 

from which we deduce the equation of thickness, 


z = 


j 7ihc x 2 ) i 
t~3~ X hw i 


7i 2 w x 

1.5w f 


( 11 ) 


404. Moments of Rectangular and Trapezoidal 
Sections. —Let DCEB, Fig. 75, be a vertical rectangular 
wall of masonry, of sectional area exactly equal to the tri¬ 
angular section of wall in Fig. 74, viz., 15 feet in height and 
5 feet in breadth, and weighing, also, 140 pounds per 
cubical foot. Let the depth of water which it is to sustain 
upon either side, at will, be 12 feet. 









400 


PARTITIONS, AND RETAINING WALLS. 


Tlie horizontal resultant of water pressure is 

= 2.25 tons, 

of weight of wall into the coef- 
[ W — (.25^)] x c = 2.96 tons. 

1 

This leaves a small margin of frictional stability. 

The vertical weight resultant is 

(Aw) — (.25Zi) = 4.78 tons, 

or, if there is no upward pressure, 

Aw = 5.25 tons. 

Plot to scale the horizontal and vertical resultants from 
their intersection in x , • and complete the parallelogram 

xPMe 2 ; then will the diagonal 
xM be the final resultant of the 
two forces. 

The direction of the diagonal 
now cuts the base very near 
the toe (7, and the given wall 
with vertical rectangular sec¬ 
tion lacks the usual coefficient 
of leverage stability, though it 
was found to have ample lever- 
age stability in the equal tri¬ 
angular section. 

If we now give to this same 
wall a slight batter upon each 
side, as indicated by the dotted lines, its final resultant, 
arising from the horizontal water pressure, will lie in x0 2 > 


Fig. 75 . 


£T 

< 


5 - O 


B 

> 





7i 2 

and the vertical resultant 
ficient (.62) of friction is 



















MOMENTS OF SECTIONS. 


401 


and its direction will cut the base farther from the toe, and 
the leverage stability of the wall will be increased. 

Let I) CEB, Fig. 76, be a section of a partition wall in a 
reservoir, subject to a pressure of water whose surface coin¬ 
cides with its top, on either side, at will. Let the height be 
12 feet, and the thickness at top 4 feet. 


Fig. 76. 



The side EC is vertical and the side BD has a batter of 
three inches to the foot. 

The maximum pressure resultants meet the respective 
sides in P and P l5 in directions perpendicular to their sides, 
and at depths equal to two-tliirds the vertical depth EC. 

26 

























































































402 


PARTITIONS, AND RETAINING WALLS. 


Plot to scale tlie horizontal pressure resultants in their 
respective directions through P and P,, and the weight 
resultant in its vertical direction through the centre of grav¬ 
ity,* 6r, and complete the parallelograms. The diagonals 
then give the directions and magnitudes of the maximum 
leverage effects. 

The diagonal xO cuts the base CD at a distance from K 
less than half KD ; the diagonal xM cuts the base at a 
distance from K more than half the distance KC. 

The leverage stability of the wall is therefore satisfactory 
to resist pressure from the left, but has not the desired 
factor of safety to resist pressure from the right. 

405. Graphical Method of Finding* the Leverage 
Resistance. —The ratio of leverage resistance may be 
obtained from the sketch by scale, as follows: Extend the 
base, JO, of the parallelogram upon the right, indefinitely ; 
draw a broken line from x through D, cutting J0r l in r x ; 
then the ratio of leverage stability against the water pressure 
upon EC is to unity as Ji\ is to JO. 

Also extend K0 2 indefinitely ; draw a broken line from 
y 2 through the toe C\ cutting K0 2 r 2 in r 2 ; then the ratio of 
leverage stability against the maximum water pressure 
upon BD is to unity as Kr 2 is to KO,. 

The ratio of r 2 0 2 to r 2 K exceeds .5, but the ratio of tM 
to rJ is less than .5; therefore the effect of the horizontal 
pressure x x P\ to overturn the wall exceeds the effect of the 
maximum pressure yP x to overturn the wall. 

406. Granular Stability. —We have found the maxi - 

• The centre of gravity of a rectangular symmetrical plane. Fig. 75, lies in 
tlie intersection of its diagonals. 

The centre of gravity of a trapezoidal plane DCEB, Fig. 76, may be found 
graphically, thus: Prolong CD to i, and make Ci — EB. Also prolong EB to 
k, and make Bk = CD. Join hi. Bisect CD and EB, in d and b, and join db. 
The centre of gravity G lies in the intersection of the lines db and ik. 





COMPUTED PRESSURE IN MASONRY. 


403 


mum water pressure resultant upon the inclined side, JO 
(Fig. 74), to be yP x = y = 2.714 tons; its direction to be 
perpendicular to JO , and its point of application to be at 
two-thirds the vertical depth JO, or iC. 

Plot this inclined resultant, in the prolongation of the 
line yP x , from a vertical through G , in y 2 P 2 = 2.714 tons; 
and plot the vertical weight resultant of the wall from the 
intersection y 2 , in y 2 K 2 = 5.25 tons ; complete the parallelo¬ 
gram y 2 P 2 0 2 K 2 , then the diagonal y 2 0 2 is in magnitude 
and direction the maximum pressure resultant of the two 
forces tending to crush the granular structure of the wall 
and its foundation. 

The following table of data relating to computed pres¬ 
sures in masonries of existing structures, is condensed and 
tabulated from memoranda* given by Stoney and from 
other sources: 


TABLE No. 8 5. 
Computed Pressures in Masonry. 


Kind of Masonry. 


Piers, All Saints Church. 

Pillar, Chapter House. 

Pillars, dome St. Paul’s Church 
“ “ St. Peter’s Church 

Aqueduct, pier. 

Arch bricks, bridge, Charing ) 

Cross.f 

Pier bricks, Suspension Bridge. 

Bridge pier. 

Arch concrete, bridge. Char-) 

ing Cross.f 

Arch bricks, viaduct. 

Brick chimney. 

Bricks, estimated pressure on ) 
leeward side in a gale. ... ) 




ts 3 M • 

« W h 

Location. 

Material. 

Pressi 

IN LBS. 
SQ. FOC 

Angers. 

Elgin. 

London. 

Rome. 

Marseilles. 

Forneaux stone. 

Red sandstone. 
Portland limestone. 
Calcareous tufa. 
Stone. 

86,016 

40,096 

39424 

33.376 

30,240 

London. 

London paviors. 

26,880 

Clifton. 

Saltash. 

Staffordshire blue bricks. 
Granite. 

22,400 

21,280 

London. 

Port. Cement, i; gravel, 7 . 

17,920 

Birmingham. 

Glasgow. 

Red bricks. 

Brick. 

15,680 

20,160 

• • • • 

• • • • 

33,600 


Long span bridges have sometimes pressures at their springing exceeding 
125,000 pounds per square foot. 


* The Theory of Strains in Girders and Similar Structures. New York, 1873. 























404 


PARTITIONS, AND RETAINING WALLS. 


Experimental data of the ultimate strength of masonry 
in large masses has not been obtained in a sufficient number 
of instances to determine a limit generally applicable for 
safe practice. 

Failure first shows itself by the spalting off of the angles 
or edges of the stones, or by the breaking across of stones 
subjected to a transverse strain, and next by the crushing 
of the mortar. 

407. Limiting* Pressures. —From experiments of sev¬ 
eral engineers upon the ultimate crushing strength of small 
cubes of dressed stones (1 inch and 1J inch square), and 
from computations of pressures upon the lower courses of 
tall stacks and spires, the data of the following table has 
been prepared: 


TAB L E No. 86. 

Approximate Limiting Ppessures upon Masonry. 



Av. weight laid 
in mortar, per 
cubic foot. 

Approx, ulti¬ 
mate resistance 
of dry, dressed, 
one-inch cubes. 

Est. safe static 
pressure per 
sq. ft. on thick 
blocks, unlaid. 

Est. safe pres¬ 
sure per sq. ft. 
in coursed rub¬ 
ble masonry, at 
2 ft. from edge, 
when laid in 
strong mortar. 

Limestone. 

152 lbs. 
132 “ 

154 “ 

120 “ 

4,000 lbs. 
6,000 “ 
10,000 “ 
2,500 “ 

115,000 lbs. 
170,000 “ 
280,000 “ 
72,000 “ 

15,000 lbs. 
15, 000 “ 
20,000 “ 
8,000 “ 

Sandstone. 

Granite. 

Brick. 



McMaster mentions* that in Spain, and in some instances 
in France, the limit of pressure in stone masonry has been 
taken in practice as high as 14 kilogrammes per square 
centimeter (= 28678 lbs. per square foot); but in the ma¬ 
jority of cases the limit is taken at from 6 kilometers to 8.50 
kilometers per square centimeter, or say 15000 lbs. per sq. ft. 


* Profiles of High Masonry Dams. New York, 1876. 






















WALLS FOR QUIET WATER. 


405 


The ultimate granular resistance of the masonry is 
largely dependent upon the strength of the mortar, and 
upon the skill applied to the dressing and laying of the 
stones. 

It is not advisable to allow either a direct or resultant 
pressure exceeding 140 pounds per square inch within one 
foot of the face of rubble masonry, or 200 pounds per square 
inch in the heart of the work; and these limits should be 
approached only when both materials and workmanship 
are of a superior class. 

The resultant of the horizontal pressure is seen to cut 
the base-line nearer to the toe, or fulcrum, over which the 
resultant tends to revolve the wall, than does the resultant 
of maximum pressure ; the crushing strain is therefore 
greater near the face of the masonry from the horizontal 
than the maximum resultant. 

Care must be exercised, in high structures, that the safe 
pressure limit near the edge is not exceeded, lest the edge 
spalt off, and the fulcrum be changed to a position nearer 
the centre of the wall, and the leverage stability thus re¬ 
duced. 

408. Table of Walls for Quiet Water. — The fol¬ 
lowing table gives dimensions for walls to sustain quiet 
water on either side, and also on the back only, with a 
limiting face batter of two inches per foot rise : 


t 


406 


PARTITIONS, AND RETAINING WALLS. 


TABLE No. 87. 

Approximate Dimensions of Walls to Retain Water. 

For granite rubble walls, in ?nortar, of specific gravity 2 . 25 , or weight, 140 pounds 
per cubic foot; to retaiti quiet water level with the top of the wall. 


Height of 
water and 
wall, in feet. 

Vertical 

Rectangular 

Wall. 

Pressure on either side. 
Symmetrical Partitions. 

Pressure on Back only. 

Breadth in 
feet. 

Top 

breadth in 
feet. 

Bottom 
breadth in 
feet. 

Top 

breadtn in 
feet. 

Face batter 
in inches 
per ft. rise. 

Bottom 
breadth in 
feet. 

4 

3-5 

3-5 

3-5 

3-5 

O 

3-5 

5 

3-5 

3-5 

3-5 

3-5 

O 

3-5 

6 

3-5 

3-5 

3-5 

3-5 

O 

3-5 

7 

4.0 

3-5 

4-25 

3-5 

i 

4.0 

8 

4-5 

3-5 

5- 2 5 

3-5 


5-o 

9 

5-° 

3-5 

6.00 

3-5 

2 

5-75 

10 

5-5 

3-5 

6.50 

3-5 

2 

<5-75 

11 

6.0 

3-5 

7-25 

3-5 

2 

7-25 

12 

6-75 

4.0 

7-75 

4.0 

2 

7-83 

13 

7*25 

4.0 . 

8.50 

4.0 

2 

8.67 

14 

7-75 

4.0 

9-25 

4.0 

2 

9-50 

15 

8.25 

4.0 

10.00 

4.0 

2 

10.50 

16 

9.00 

4.0 

io-75 

4.0 

2 

11.50 

17 

9-5o 

4.0 

11.67 

4.0 

2 

12.00 

18 

10.00 

5-° 

n-75 

5-o 

2 

12.50 

!9 

10.50 

5-o 

12.67 

5-° 

2 

I3-67 

20 

11.00 

5-o 

13-33 

5-° 

2 

14.50 

21 

11.50 

5-o 

14.00 

5-o 

2 

I5-25 

22 

12.25 

5-o 

14.83 

5-o 

2 

16.25 

2 3 

12.75 

5-° 

15-75 

5-o 

2 

I7-25 

24 

13-25 

5-o 

16.50 

1 

5-o 

2 

18.25 


The top thickness is to be increased if the top of the 
wall is exposed to ice-thrust; and the whole thickness 
must be increased if water is to flow over the crest, accord¬ 
ing to the depth of the crest, and its initial velocity of ap¬ 
proach. 

Unless partition-walls rest on solid rock, or on impervi¬ 
ous strata of earth, as they should, percolation under the 




























ECONOMIC PROFILES. 


407 


wall must be prevented by a concrete or puddle stop-wall, 
or by sheet-piling; or the previous strata must be effectu¬ 
ally sealed over. 

409. Economic Profiles.—It is evident, from the 
above investigations, that the profile has an important influ¬ 
ence upon the leverage stability of a wall of given weight 
of material, and therefore, for a given stability, upon econ¬ 
omy of material. 

The leverage stability against pressures of water upon 
the vertical sides of triangular or trapezoidal sections of 
masonry is greater than the leverage resistances to pressures 
upon their inclined sides, as is graphically illustrated in the 
above sketches; hence there is an advantage in giving all 
the batter to the side opposite to the pressure. 

The vertical rectangular sections are least economic, and 
the triangular sections most economic of material. 

When some given thickness is assumed for the top of a 
retaining wall, to give it stability against frost, or displace¬ 
ment from any cause, then theory makes both sides vertical 
from the top downward until the limiting ratio of leverage 
stability is reached, and then gives to the side opposite to 
the pressure a parabolic concave curve. 

It may be necessary to widen the base of high,walls 
upon both sides beyond the breadth required for leverage 
stability, to distribute the weight sufficiently upon a weak 
foundation. Practical considerations, in opposition to 
theory, tend to rectangular vertical sections. 

The engineer who is familiar with both theory and prac¬ 
tice, adjusts the profile for each given case, so as to attain 
the requisite frictional, leverage, and granular stabilities, in 
the most substantial and economical manner, having due 
regard to the quality and cost of materials, and the skill 
and cost of the required labor. 


408 


PARTITIONS, AND RETAINING WALLS. 


410. Theory of Earth Pressures. —Earth filling of 
the different varieties behind retaining walls, is met in all 
conditions of cohesiveness between that of a fluid and that 
of a solid. 

The same filling, in place, is subject to constant changes 
in its degree of cohesion, as its moisture is increased or 
diminished, or as its pressure and condensation is increased* 
or as it is subjected to the tremulous action of traffic over it. 
The theory of earth pressure, therefore, leads to less certain 
results than does the theory of water pressure. 

We have seen (§ 353) that different earths have dif¬ 
ferent natural angles of repose when exposed to atmos¬ 
pheric influences, and they also tend to assume their natural 
f rictional angle when deposited in a bank. If we make a, 
broad fill with earth, behind a vertical wall and then sud¬ 
denly remove the wall, a portion of the earth, of triangular 
section, will at once fall, and the slope will assume its natu¬ 
ral frictional angle. If we make such a fill even with the 
top of a vertical rectangular wall, whose thickness is only 
equal to one-fourtli of its height, then the earth will over¬ 
turn the wall. This is evidence that a portion of the earth, 
produces a lateral pressure. If the earth is fully saturated 
with water, its lateral pressure may be nearly like that of a 
fluid of equal specific gravity. If the earth is compact like 
a solid, its thrust may be nearly like that of a rigid wedge. 

Let LBBf Fig. 77, be an earth-fill behind a vertical 
retaining wall BB. Let LBV v be the natural frictional 
angle = </>, of that earth filling. It is evident that the por¬ 
tion of earth LD V x will produce no thrust upon the ma¬ 
sonry, because it would remain at rest if the wall was 
removed. Suppose all the filling above D V l to be divided 
into an infinite number of laminae whose planes of cleavage 
all meet at one edge in D, and radiate from B. Then the 


THEORY OF EARTH PRESSURES. 


409 


thin lamina adjoining D V x will exert the minimum thrust 
against the masonry and the maximum weight-pressure 
upon D Vi. The thin lamina adjoining BD will exert the 


Fig. 77 . 



maximum wedge-thrust against-the masonry and minimum 
weight-pressure upon D V x . 

Suppose the mass V x DBJ to he divided into two parts 
















410 


PARTITIONS, AND RETAINING WALLS. 


by the plane BJ , which bisects the angle BB F- Let the 
wedge BBJ , then be increased in dimensions by revolving 
the side JB to the right, around I ); then its weight, as a 
solid, will rest more upon F, B, and its lateral thrust will 
not be increased. Let the w T edge BBJ , then be reduced in 
dimensions by revolving the side JB to the left; then its 
total weight and its ability to produce lateral thrust upon 
the masonry will be reduced. We may therefore assume 
that that portion of the mass F BBJ, included in the upper 
wedge formed by bisecting the angle V X BB will be the 
maximum portion of the earth that will first fall if the wall 
is suddenly removed, and that the thrust of the wedge BBJ , 
if considered alone, and as devoid of friction upon the plane 
JB, will give a safe theoretical maximum effect upon the 
masonry of the whole mass F BBJ. 

The practical value of such assumption has been ably 
demonstrated by Coloumb, Prony, Canon Moseley, Ran- 
kine, Neville, and others. 

411. Equation of Weight of Earth-Wedge. —The 

weight W 2 of the wedge of earth (considered as one foot 
in length), in pounds, equals its surface area BBJ, , in square 
feet, = A 99 into the weight of one cubical foot of the mate¬ 
rial = w 2 . 

W 2 = A 2 w 2 . (12) 

Let the symbol of the frictional angle LBV of the 
earth filling be </>, and of V x BJ\>q t ; then will the angle 

bdj = 0 -~a = | 1= 0 = an s le y^>J= v. 

Let the height BB equal 12 feet, = h ; then the area of 
BBJ w T ill equal BB into one-half BJ = 

li h 2 

A 2 — h x ^ tan d = cotan (<!> + <?). (13) 




PRESSURE OF EARTH-WEDGE. 


411 


412 , Equation of Pressure of Earth-Wedge.— 

Assume the weight of the wedge DBJ = A 2 w 2 — W 2 to he 
gathered into its vertical resultant passing through its cen¬ 
tre of gravity, g ; then the thrust P of the wedge equals 
its weight into its horizontal breadth BJ\ divided by its 
vertical height BD = 

P — A 2 w 2 tan 0 = W 2 cotan (0 + <f). (14) 

Draw the vertical resultant TV to scale in eP, meeting 
the inclined plane JP >, in P. 

The thrust effect of W 2 will have its maximum action in 
a line parallel to the line D V x , since the mass V X DBJ , as 
a whole, tends to move down the plane V X D. 

The theoretical reaction from the wall, necessary to sus¬ 
tain W 2 , will then be in a direction parallel to D V , cutting 
the vertical resultant in P. Draw the reaction of the wall 
to scale in nP. The reaction of the plane JD is in direc¬ 
tion and magnitude equal to the diagonal Py, of the paral¬ 
lelogram of which JV 2 and P form two sides. Draw the 
reaction of JD to scale in VP. Then will the three result¬ 
ants eP , nP, and VP be in equilibrium about the point P. 

Det 0 = 30°. 

Assume the filling to be of gravel, weighing 125 pounds 
per cubic foot, and that after a storm, its drains being 
obstructed, its voids are filled with water, increasing the 
weight to 140 pounds per cubic foot, = w 2 ; then 

W 2 = -g- cotan (0 + (f) w 2 = -g— . tan —g— 

12 

= 12 feet x feet x .57735 x 140 pounds 
= 5,820 pounds = 2.91 tons. 

The reaction from the wall necessary to sustain the 
weight of the wedge JBD = 




412 


PARTITIONS, AND RETAINING WALLS. 


P = W 2 tan 0 — — cotan 2 (</> + <p) (15) 

£ 

= 2.91 tons x .57735 
= 1.68 tons. 

The horizontal effect of P = 

x — P cos 0 = A 2 w 2 tan 6 cos $ (16) 

= 1.68 tons x .86602 = 1.45 tons. 

The thrust of the wedge tending to push away and to 
overturn the wall is equal to the reaction from the wall 
necessary to sustain the wedge in position. We find its 
horizontal effect in this case to be 1.45 tons, and this is the 
maximum effect, = x , tending to displace the wall hori¬ 
zontally. 

413. Equation of Moment of Pressure Leverage. 

—The maximum moment of pressure leverage , L , tending 
to overturn the wall around its toe, equals x into the height, 
in feet, above P at which x meets the wall. 

When the wall is vertical and the surface of filling hori¬ 
zontal, x always meets BD at one-third li from _Z), = |; 

therefore the equation of moment of pressure leverage 
becomes 

A = x - = ( A 2 w 2 tan 6 cos </>) ^ (17) 

o o 

19 ft 

= 1.45 tons x —^ = 5.80 tons. 

O 

• 

414. Thickness of a Vertical Rectangular Wall 
for Earth Pressure. —The moment of weight leverage of 

JiPw 

a vertical rectangular wall is —, in which z is the thick- 

£ 


ness of the wall. 




SURCHARGED EARTH-WEDGE. 


413 


Tlie double moment of pressure leverage of eartli level 
with the top of the wall is 

h h s 

(h 2 w 2 tan 2 6 cos 0 ) x — = — w 2 tan 2 6 cos c b. 

o 6 

When the wall just balances the theoretical double 
pressure of the earth level with its top, 

hzho h 3 , o . 

= —- w 2 tan 2 6 cos 0 , 

from which is deduced the equation of thickness for a ver¬ 
tical rectangular Avail, 


j 2 7i 3 w 2 tan 2 6 cos 0 j 

11 1 

j h 2 w 2 tan 2 6 cos 0 \ 

( 3 hw j 

r _ 1 

1.5w i 


(18) 


415. Surcharged Earth-Wedge. —When the earth- 
fill behind a wall is carried up above the top level BJ of 
the wall, and is sloped down against the top angle B, or 
upon the top of the wall, the fill DBF is then termed a 
surcharged fill. 

Its weight W 2 is, as in the case of the level fill, per lineal 
foot, 

W 2 = A 2 w 2 . (19) 

To compute the pressure of the surcharged fill, we may 
divide the mass ViDBF into two wedges by a plane DF , 
bisecting the angle V L DB, and take the action of the wedge 
FDB as equivalent to the effective action of the whole mass 
VDBF. 

Let the natural frictional angle of the earth-fill be 

0 = 30°. 

The area A 2 of the wedge FDB may be computed by 
any method of ascertaining the area of a triangular super- 





414 


PARTITIONS, AND RETAINING WALLS. 


flees. If, with a given slope BF, the till does not rise as 
high as F, and its surface level cuts FB and FJ between 
the levels of F and B , then its area is ascertained by any 
method of ascertaining the snperhees of a trapezium. 

Let fall upon DF a perpendicular from B , meeting BF 
in i ; then the distances Bi and IF are equal, each, to the 

0QO _ . 

cosine of the angle BBF = cos. —^—- = cos 0 ; and the 

distance iB is equal to sin ~ = sin 6 - 

Let the height BB = h — 12 feet. 

The area BBF equals the length BF into one-lialf iB = 

A 2 = h x 2 cos 6 x h \ sin 6 = 7i cos 0 x It sin 0 (20) 

= (12 x .866) x (12 x .5) = 62.53 sq. ft. 

Let the mean weight of the fill, which is quite sure to be 
drained above the level BJ, be assumed 13d pounds per 
cubical foot. 

* 

416. Pressure of a Surcharged Earth-Wedge.— 

Suppose the weight to be gathered into its vertical resultant 
passing through the centre of gravity of the mass BFB. 
This vertical resultant will meet the plane FB in P Y at a 
level higher than P. 

The wedge-thrust P 1? due to the weight W 2 , equals the 
weight into the horizontal breadth BJ , divided by the 
height BB = 

QO° W* 

Pi = W 2 tan —-— = A 2 2C 2 cotan ($ + g>)= (21) 

62.53 sq. ft. x 130 lbs. x .577 = 4690.38 lbs. = 2.345 tons. 

The maximum pressure-action of the weight upon the 
w T all is in a direction parallel to T \B, the natural frictional 
angle 0, of the filling material. Its horizontal pressure 
effect , Xi, is therefore: 





PRESSURE OF AN INFINITE SURCHARGE. 


415 


x x = P x x cos 0 = A 2 w 2 tan 0 cos 0 = ( 22 ) 

2.345 tons x .866 = 2.03 tons. 

The maximum horizontal pressure resultant takes its 
direction through P x and meets the wall at the altitude of 

P„ which is greater than 

We may here observe that, even though the fill DBF 
is of lighter material than the fill DBJ \ so that the total 
weight of one is exactly equal to the total weight of the 
other, the pressure leverage effect from the surcharged fill 
will exceed the pressure leverage effect from the level fill, 
because its centre of gravity g 2 will be higher than g , its 
vertical resultant W 2 will meet the plane JD in P x at a point 
higher than P, and its horizontal resultant x x will meet the 
wall at a greater altitude from D than will the resultant x. 

Let r h be the symbol of the ratio of h at which x x meets . 
the wall from D ; then if x x meets DB at J h , r h = .3333 ; 
and if x x meet DB at \h, r h = .5, etc. 

417. Moment of a Surcharge Pressure Leverage. 
—The maximum moment of pressure leverage L x , of a sur¬ 
charged fill, tending to overturn the wall around its toe, 
equals x x into the height, in feet = (r h h) above P, at which 
x x meets the wall. 

L x =x x x (r h h) = A 2 w 2 tan 6 cos 0 (rji) — (23) 

2.03 tons x 5.98 = 12.14 tons. 

418. Pressure of an Infinite Surcharge.— Let PP, 

Fig. 78, be the natural slope of the filling material, and 
parallel with DI, which makes with DL the natural fric¬ 
tional angle LDI — 0 . Let BF extend indefinitely. 

If IDBF is a perfect solid it will be just upon the point 
of motion down the slope ID ; on the other hand, if IDBF 


416 


PARTITIONS, AND RETAINING WALLS. 


is liquid, of specific gravity equal to the specific gravity of 
the filling material, it will then exert its maximum pressure 
upon the wall-face DB. 

Let the filling be considered liquid, resting upon the 
equivalent horizontal base DI, and having the equivalent 
horizontal surface BF 

Let fall upon DI a perpendicular from B, meeting DI 
iny; then will Bj be an equivalent vertical projection, or 
trace, of BD. The angle BBj equals the angle LI)I = 0. 
The distance Bj = 7 ^ 1 equals the distance BD (=Ji) into the 
cosine of the angle DBj = h cos 0 . 


h 2 

The direct liquid pressure P x upon Bj equals — w 2 = 

/d 



and the pressure upon BD in the same direction is 


7^ 2 

= w 2 — cos 2 0 , 

/d 


and its maximum resultant has a direction parallel with 
ID, and meets Bj at one-tliird the height jB, in m, and BD 
at one-third the height DB, in P x . 

The horizontal pressure effect x x upon the wall BD, is 

h 2 

x x = P x cos 0 = w 2 — cos 3 0 = (25) 

/d 

102 

130 lbs. x — x .6405 = 6079.32 lbs. = 3.036 tons. 


The maximum moment of liquid pressure leverage L x 
of the infinite surcharged fill tending to overturn the wall 
around its toe, equals x x into one-third the height BD. 


A = 3. 4 = 1 

3.036 tons x 


w, 


7i 2 


2 

12 ft. 


cos 3 0 ) x —■ — 

' O 

— 12.14 tons. 


(261 


3 




RESISTANCE OF MASONRY REVETMENTS. 417 

419. Resistance of Masonry Revetments. —The 

elements of stability of a revetment that enables it to sus¬ 
tain the thrust of an earth-tilling behind it, are identical 
with those we have already examined (§ 401), that enable 
it to sustain a pressure of water. 

There must be sufficient weight, W, to give it frictional 
stability, 8, and the profile must be adjusted so that with 
the given weight the mass shall have the requisite moment 
M of weight leverage, with an ample coefficienty of safety, 
to resist the thrust of the earth-filling, at its maximum. 

The iceiglit of wall above any given horizontal plane 
between B and I) (Fig. 77) equals the area of the section 
above that plane in square feet, into the weight of a cubical 
foot of the materials of the wall (§ 398), 

= W= Aw. 

The frictional stability , 8, of the wall at the given hori¬ 
zontal plane, that has to resist the horizontal pressure of 
the earth filling, equals the weight of masonry above that 
plane, plus the vertical downward pressure of any water 
that may rest upon its front batter (BJC, Fig. 80), less the 
vertical resultant of upward pressure beneath the plane or 
in the bed-joints, and into the coefficient of friction of the 
given section upon its bed (§ 398), 


8 — (TF T c — C\Z\) . c. 

The moment of weight leverage of the wall that has to 
resist the overturning tendency of the earth-thrust, equals 
the weight of the masonry above the given plane into the 
horizontal distance of the centre of gravity of the masonry 
from the toe, or fulcrum, over which the thrust tends to 
revolve it (§ 402), 

M — Awd. 


27 


418 


PARTITIONS, AND RETAINING WALLS. 


In these equations: 

W is the weight above the given plane. 

S “ “ frictional stability of the given section. 

M “ “ moment of weight leverage of the given section. 
e “ “ vertical downward water pressure resultant. 
z x “ u vertical upward water pressure resultant. 
c l “ “ ratio of effective vertical upward water pressure. 
c “ “ coefficient of friction of the given section upon 
its bed. 

The moment of w T eiglit leverage of the wall must, for a 
safe coefficient of stability, be equal to double the moment 
of pressure leverage of the earth fill; that is, for a level fill 
we must at least make 

Awd a ± a , h 
——— = A 2 w 2 tan. 0 cos. -> 

2 O 

and for a surcharged fill, 

4^ — A 2 w 2 tan. 0 cos. </> ( r h 7i), 

and a like margin of frictional stability should be secured. 

420. Final Resultants in Revetments, —The height 
of the wall (Fig. 79) is the same, by scale, as the wrnll in 
Fig. 77, whose reactions to sustain the level and surcharged 
fills we have investigated. 

The back of the wall (Fig. 79) is vertical, and the hori¬ 
zontal earth-tlirusts against it are as before computed—viz., 
1.45 tons for the level fill, and 2.03 tons for the surcharged 
fill. Draw these horizontal eartli-tlirust resultants to the 
left from a vertical line passing through the centre of gravity 
of the masonry, in their respective directions and at their 
respective altitudes. Draw in the vertical line the vertical 
weight resultant of the masonry in PK; complete the paral¬ 
lelogram PK0_x; then will the diagonal P0 2 represent, in 




TRAPEZOIDAL REVETMENTS. 


419 


magnitude and direction, the resultant effect of the level fill 
LDBJ. 

Draw the vertical weight resultant of masonry, also, in 
P s e 2 , and complete the parallelogram P i e 2 Mx i3 ; then will the 
diagonal P 3 df represent, in magnitude and direction, the 
resultant effect of the surcharged fill LDBF. 

The comparative thrust effects of the level and sur¬ 
charged fills upon the masonry are shown by the positions 
of the respective final resultants, and the comparative re¬ 
sistances of the wall against each, by the distances from 
O, at which their directions cut the plane CD. 


Fig. 79, 



421. Table of Trapezoidal Revetments. —The fol¬ 
lowing table of dimensions of walls, to sustain earth, in 
which the sections are trapezoidal, and face batters limited 
to two inches per foot rise, is adapted for walls to sustain 
gradings about pump-liouses, reservoir-grounds, etc., and 
will give approximate dimensions for plotting trial sections 
when it is desired to resolve the profile into other forms. 

















420 


PARTITIONS, AND RETAINING WALLS. 


TABLE No. 88. 

Approximate Dimensions of Walls to Sustain Earth. 

For granite rubble walls , in mortar, of specific gravity 2 . 25 , or weight 140 pounds 
per cubic foot, to retain earth level with the top of the wall. 


Height of wall, 
in feet. 

Top breadth of 
wall, in feet. 

Face batter of 
wall, in inches 
per foot rise. 

Base breadth of 
wall at lower earth 
surface, in feet. 

Thickness of a 
vertical rectangular 
wall, in feet. 

4 

3 • 0 

O 

3 -o 

3 -o 

5 

3 • 0 

O 

3 -o 

3 -° 

6 

3 - 0 

O 

3 ° 

3 -° 

7 

3 • 0 

O 

3- 2 5 

3 - 5 ° 

8 

3 • 0 

1 

2 

3 • 83 

4.00 

9 

3-33 


4-83 

425 

10 

3-33 


5.0° 

4 - 5 ° 

11 

3-5 


5- 2 5 

5.00 

12 

3*5 

2 

5- 6 7 

5 - 5 ° 

13 

3-5 

2 

6-33 

5 • 83 

14 

3-5 

2 

7.00 

6.25 

15 

3-5 

2 

7 - 5 ° 

6 -75 

16 

4.0 

. 2 

8.00 

7-25 

17 

4.0 

2 

8.67 

7-75 

18 

5 -° 

2 

9.00 

8.25 

*9 

5 -o 

2 

9 - 5 ° 

8-75 

20 

5 *° 

2 

9.87 

9.00 

21 

5 -o 

2 

10.50 

9 - 5 ° 

22 

5 -° 

2 

11.00 

to. 25 

23 

5 ° 

2 

n -33 

10.50 

24 

5 -° 

2 

11.78 

i °-75 


It will rarely be advisable to reduce tlie top thicknesses 
given in the table, with a view only to economizing ma¬ 
terial lest the top courses be too light to withstand the 
variety of shocks to which they will be liable, and which 
are not recognized in the common formulas. 

Several eminent professors who have written upon the 
theory of retaining walls, give formulas for determining their 
proportions ; but such formulas usually give too small top 
breadths, for practical adoption, for low walls, and objec¬ 
tionably great top breadths for high walls. 


















CURVED FACE—BATTER EQUATION. 


421 


Each class of wall lias its own most convenient top 
"breadth, which remains nearly constant through a large 
range of height. 

Common uncoursed rubble walls of granite, laid dry, 
should be increased from the above dimensions six inches 
in the top breadth and thirty-three per cent, in the bottom 
breadth. If the level earth-filling behind the wall is to be 
loaded, or subject to traffic, the weight and leverage resist¬ 
ance of the wall are to be increased accordingly. 

The thrust of the filling material behind a retaining wall, 
upon the wall, will be lessened if the filling next the wall 
is spread in thin horizontal layers and well settled, instead 
of being allowed to slope against it, as it falls at the head 
of a dump. 

4 : 22 . Curved Face—Batter Equation. —When it is 
desired to give to the face a curve, the back being perpen¬ 
dicular, and the top breadth constant, the following equa- 

* 

tion will assist in determining ordinates at any given depths 
for plotting a trial section. 

Let 1) be the assumed toj) breadth, and t the thickness 
at any given depth cZ, then 

t = b + .75 VdK (27) 

For illustration, assume the top breadth not less than 
3.5 feet; then for several given depths, from 0.0 to 30 feet, 
we have ordinates, or thicknesses, as given in Table No. 89. 

Upon the curve thus obtained, steps may be laid off with 
either vertical or battered risers. 

Tests with the equation for moment of leverage stability, 
will determine whether the risers may cut the curve, or if 
the inner angle of tread and riser shall lie in the curve. 

A slight increase or reduction of the top breadth, or of 
the fractional multiplier, will increase or reduce the wall- 
section, as desired. 


422 


PARTITIONS, AND RETAINING WALLS. 


TABLE No. 89. 

Thickness at Given Depths of a Curved Face Wall. 


Depths. 


Thickness. 

• 

Feet. 

( 3 .) 


•75 VcP 


Feet. 

O 

3-5 

+ 

.O 

— 

3 - 5 ° 

4 

3-5 

+ 

.6 


4.10 

6 

3-5 

+ 

I.IO 

— 

4.60 

8 

3-5 

+ 

1.69 

— 

5* x 9 

IO 

3-5 

+ 

2 -37 


5- 8 7 

12 

3-5 

+ 

3. 12 

— 

6.62 

*5 

3-5 

+ 

4 - 3 6 

— 

7.86 

20 

3-5 

+ 

6.71 

— 

10.21 

2 5 

3-5 

+ 

9*38 

— 

12.88 

3 ° 

3-5 

+ 

12.32 

— 

I 5 - 82 


423. Back Batters, and their Equations. —When 

for practical or other reasons there is objection to giving all* 

> 

the batter to the front of the wall, and a portion of it is 
placed upon the back, then it is usually arranged in a 
series of offsets or steps BD X , Fig. 80. 

In such case, the weight of the triangle of earth B 2 D i B 
may be assumed to be supported entirely by the Avail, and 
as producing no lateral thrust upon the wall. This triangle 
increases the Aveiglit leverage of the wall, and moves its 
Aveiglit resultant farther back from the toe C. 

Find the centre of gravity of the masonry, in g, and find 
the centre of gravity of the triangle of earth, in g 2 ; then will 
the centre of gravity of the two united bodies be in G. 

Let LD X I be the natural frictional angle of the material. 
Bisect the angle ID X B 2 by the plane D X F ; then we may 
assume the trapezium B X B 2 F X F to be that portion of the 
earth-filling that, considered alone, will produce the maxi¬ 
mum thrust effect upon the AA T all, and its horizontal and 
leverage effects may be computed by equations 21 and 23. 









INCLINATION OF FOUNDATION. 


423 


Fig. 80. 



Prof. Moseley’s equation * for tlie maximum pressure of 
a surcharge similar to this is 

P\ = \7h sec </> — (7h 2 tan 2 </> -f c 2 2 )^ 2 , (28) 

in which c 2 is the height B 2 c 2 . 

Pi “ maximum pressure of the earth. 
w 2 “ weight of one cubic foot of earth. 
hi ‘ vertical distance jDiC 2 . 

<P “ frictional angle of the earth. 

424. Inclination of Foundation. — The frictional 
stability of a wall upon its foundation is materially in- 


* Mechanics of Engineering, p. 426. Van Nostrand, New York, 1860. 





































424 


PARTITIONS, AND RETAINING WALLS. 


creased, and its pressure is more evenly distributed upon 
tlie foundation stratum, if an inclination is given to the bed 
nearly at right angles to the final thrust resultant, as in 
Fig. 80. Bed-joints may often be similarly inclined with 
advantage. 

A sliding motion in such case involves the additional 
work of lifting the whole weight up the inclined plane. 

425. Front Batters and Steps. —Masons experience 
a very considerable difficulty in laying the face of rubble 
walls with batters exceeding two inches to the foot, and 
often with batters exceeding one and one-lialf inches to the 
foot, unless with stones from a quarry where the transverse 
cleavage varies several degrees from a perpendicular to 
the rift. 

The difficulty is increased when the bed-joints of the 
work are level from front to rear, as the workmen prefer to 
make them. 

it is especially troublesome to the workmen, and expen¬ 
sive as well, to make face-batters of high walls conform to 
the theoretical curved batters deduced from the logarithmic 
equations. 

It is better, therefore, to transpose the curve into a series 
of steps when its tangent inclination exceeds two inches to 
the foot, in which case the steps may have equal heights 
and varying projections, as in Fig. 81, which is a revetment 
upon a navigable river, or may have both varying rise and 
projection, with batter upon the rise, as in the weir, Fig. 72. 

426. Top Breadths. —The thickness at the top of a 
revetment should in all cases be sufficient, so that its weight 
will be able to resist the frost expansion thrust of the sur¬ 
face layers of the earth. Sometimes a batter is given to the 
back of the wall, three or four feet down from the top, to 
enable the earth to expand readily in a vertical direction, 


26 — FEET, 


TOP BREADTHS. 


and thus act with less force horizontally against the backs 
of the cap-stones. 

An increased thickness at the top of the wall, and at all 
points of depth, is also necessary when the filling is liable 
to be loaded with construction materials, fuel, merchandise, 


Fig. 81. 

E ll 



or other weights, or if it is to sustain traffic of any kind. 
The additional weight may in such case be considered 
equivalent to a surcharge weight, and the centre of gravity 
of the filling and of the additional weight will be resolved 
into their united centre of gravity and the vertical resultant 






































426 


PARTITIONS, AND RETAINING WALLS. 


Ibe considered as passing through this new centre of gravity. 
The new horizontal thrust resultant will then act upon the 
wall at a greater altitude, and with greater leverage than 
the horizontal resultant of tilling alone (§ 416), as has 
been already demonstrated. 

In the cases of discharge weirs the floods are considered 
as surcharge weights, and not only the depth of water 
behind the weir and upon its crest is to be considered, but 


Fig. 82. 



the additional height to which the velocity of approach of 
the water is due. 

If there is but one or two feet depth of water flowing 
over, then the cap-stones may be subject to the blows of 
logs, cakes of ice, and such debris as the floods gather. 

427. Wharf Walls. —When a wall is to be generally 





















































ELEMENTS OF FAILURE. 


427 


used for wharf purposes, its face should be protected by 
fender piles, both for its own advantage and that of the 
vessels that lie alongside. 

Fig. 82 illustrates the method of piling and capping, 
adopted by the writer, in an extensive wharf-'pier of one- 
lialf mile frontage in one of the deep harbors upon the New 
England coast. The caps are, in this case, dressed dimen¬ 
sion stones, three and one-lialf feet wide and one foot thick. 
The wharf log is made up of 12" x 10" and 12" x 8" hard 
pitch pine, placed one upon the other so as to break joints, 
and tre-nailed together. The anchors of the pile-heads pass 
through the cap-log, and their bolts pass through the cap¬ 
stones into headers specially placed to receive them. The 
piles are placed eight feet between centres, and each fourth 
pile extends above the log for a belay pile. Waling 
pieces of 6 " x 12" hard pine are fitted between the pile-heads, 
and spiked to the face of the cap-log to confine the pile- 
heads rigidly in place. Midway between the belay piles 
are belay rings, whose bolts pass through the cap-logs into 
headers, and are also anchored by straps to cap-stones. 

428. Counter-forte d Walls. —There is so rarely an 
economic advantage in counter-forting a wall, except in 
those cases of brick walls where the counter-fort may take 
the form of a buttress upon the exterior face, that we shall 
not here devote space to their special theoretical investiga¬ 
tion, which, by graphical analysis, is a simple reapplication 
of the principles already laid down. 

429. Elements of Failure. —In our theoretical inves¬ 
tigation of the resistances of masonry to sliding or overturn¬ 
ing we have supposed the walls to be laid in mortar and 
solid, and well bonded, so that the mass was practically 
one solid piece, considered as one foot long. 

If any given foot of length, considered alone as a unit 


428 


PARTITIONS, AND RETAINING WALLS. 


of length, is found stable, and each other foot is equal to it, 
then evidently the whole length will be stable. 

The joints from front to rear in cut and tirst-class rubble 
walls are usually laid level, and the workmen intend to give 
a good bond of one course upon another. When consider¬ 
ing the leverage stability of a high wall, at the respective 
joints, working from top downward, we usually treat the 
joints as horizontal planes. Let us turn again to the sketch 
of the partition wall, Fig. 76, which has joints laid off upon 
it showing an average class of rubble work. Suppose the 
water to be drawn off from the side and the full water 
upon the opposite side to be freezing, and the ice exerting a 
thrust upon the upper courses of the wall. We investigate 
the leverage stabilty at the joint jj\, and find that it will 
resist a considerable leverage strain, which for further illus¬ 
tration we assume to be ample. Examining critically the 
building of the wall, we find that jj\ is not the real joint, 
and j\ the fulcrum to be considered in connection with 
pressure upon Bj, but in consequence of faulty workman¬ 
ship, jj 2 j\ is the zigzag joint and the fulcrum, and that 
the joint, instead of being horizontal, is an equivalent in¬ 
clined plane on which the wall is quite likely to yield by 
slipping slightly with each extra lateral strain put upon it. 

If in a high and long wall such weaknesses are repeated 
several times, the result will be a bulge upon the face of 
the wall, ordinarily reaching its maximum at about one- 
third the height of the wall, the portion above that level 
appearing to have been moved bodily forward, and retain¬ 
ing nearly its true batter. 

When walls are so high as to require a thickness in a 
considerable portion of their height exceeding seven or 
eight feet, careless wall-layers, who are not entitled to the 
honorable name mechanic , often pile up an outside and 


FACED, AND CONCRETE REVETMENTS. 429 

inside course, and fill in the middle with their refuse stone, 
thus producing a miserable structure, especially if it is dry 
rubble, that is almost destitute of leverage stability, unless 
a great surplus of stone is put into the wall sufficient to 
resist the thrust of an earth-backing by compounded weight 
alone. 

Short walls supported at each end may by, such trans¬ 
verse motion be brought into an arched form, concave to 
the pressure, but at the same time into a state of longitudi¬ 
nal tension that will assist in preventing further motion. 

If there is the least transverse motion in a mortared wall 
sustaining water, the masonry ceases from that instant to 
be water-tight, and if the stones are in the least disturbed 
on their bed after their mortar has begun to set, the wall 
will never be tight. 

430. End Supports. —Well constructed short walls, 
supported at each end, such as gate-chamber and wheel-pit 
walls, have an appreciable amount of that transverse resist¬ 
ance prominently recognized in a beam, which permits 
their sections to be reduced, an amount dependent on the 
effective value of such transverse support. The supported 
ends of long walls transmit the influence of the support in a 
decreasing ratio, out to some distance from the supports, 
and walls wdiose ends abut upon inclines, as in the case of 
stone weirs across valleys, may be reduced in thickness, 
ordinarily, at the top and through their whole height, as 
the height reduces. 

431. Faced, and Concrete Revetments. —Walls on 
deep water-fronts, as in Fig. 81, for instance, when laid 
within coffer-dams, are often faced with coursed ashler 
having dressed beds and builds, and backed up with either 
rubble-work laid in mortar, or with concrete, the headers of 
the ashler being intended to give the requisite bond between 


430 


PARTITIONS, AND RETAINING WALLS. 


the two classes of work. Much care must be exercised in 
such composite work, lest the unequal settlement of the 
different classes of work entirely destroy the effective bond 
between them and thus lead to failure. 

Such walls have been constructed with perfect success 
without coffer-dams, of heavy blocks of moulded beton , and 
also successfully by depositing concrete in place in the wall, 
under water, with the assistance of a caisson mould, or 
sheet-pile mould, thus forming a monolithic revetment. 

Foundations under water to receive masonry structures 
have also been successfully placed by the last-mentioned 
system. 

Concrete structures under water laid without coffers, 
however, demand the exercise of a great deal of good judg¬ 
ment, educated both in theory and by practice, and admit 
only of the most faithful workmanship. 







Fig. 83. Fig. 84. 





Fig. 89. 




n / 2 3 4- 5 6* 7 & 9 /O // Z 2 

».;■ ! ! i i ■ i -i— ) 


CONDUIT SECTIONS. 


















































































































































CHAPTER XX. 


MASONRY CONDUITS. 

432. Protection of Channels for Domestic Water 
Supplies. —The observations, sound reasonings, and good 
judgments that influence municipalities to seek and secure 
the most wholesome and coolest waters for their domestic 
uses, compel them also to guard the purity and maintain 
the equable temperature of the waters as they flow to the 
point of distribution. 

The larger cities, with few exceptions, must lead their 
waters in artificial conduits, from sources in distant hills, 
where neither the soils nor atmosphere are tainted by 
decompositions such as are always in progress in the midst 
of large concourses of human beings and animals. 

Such long water-courses ought to be paved or revetted, 
or their currents will be impregnated with the minerals 
over which they flow, and will cut away their banks where 
the channels wind out and in among the hills. An arch of 
masonry spanning from wall to wall is then the most sure 
protection from inflowing drainage, the approach of cattle 
and vermin, the heating action of the summer sun, and the 
growth of aquatic plants in too luxuriant abundance. 

433. Examples of Conduits. —When proper grades 
are attainable to permit the waters to flow with free sur¬ 
faces, such conduits, requiring more than six or eight square 
feet sectional area are usually, and most economically, con¬ 
structed of hydraulic masonry. 


432 


MASONRY CONDUITS. 


Figures 83 to 89 illustrate some of the forms adopted in 
American masonry conduits. 

Fig. 87 is a section of the Croton conduit, at a point 
where it is raised upon embankment. This conduit is 7-5" 
wide and 8-5J" high, and conveys from Croton River to the 
distributing reservoir in Central Park, New York city, 
about one hundred million gallons of water daily. The 
combined length of conduit and of siphons between Croton 
Dam and Central Park is about thirty-eight miles, and they 
were completed in 1842. 

Fig. 88 is a section of the Washington conduit, which is 
circular, of 9 feet internal diameter. This leads water from 

i 

a point in the Potomac River about sixteen miles from the 
capital, to a distributing reservoir in Georgetown, from 
whence the water is led to the Government buildings and 
grounds, and throughout the City of Washington, in iron 
pipes. This conduit was constructed in 1859. 

Fig. 84 is a section of the Brooklyn, L. I., conduit lead¬ 
ing the waters of Jamaica and other ponds to the basin ad¬ 
joining the well of the Ridgewood pumping-engines. This 
conduit increases in dimensions at points where its volume 
of ilow is augmented from 8 -2" wide to 10-0" wide, and to 
a maximum height of 8 -8". It was constructed in 1859. 

Fig. 86 is a section of the Charlestown, Mass., conduit, 
leading the water of Mystic Lake to the well of the Mystic 
pumping-station. This conduit is 5-0" wide and 5-8" high, 
and was constructed in 1864. 

Fig. 85 is a section of the Lowell, Mass., conduit, of 
4-3" diameter. This leads water from a subterranean 
infiltration gallery along the margin of the Merrimack 
River, a short distance above Lowell, a portion of the dis¬ 
tance to the pumping-station. It was constructed in 1872. 

Fig. 89 is a section of the second Chicago tunnel, extend- 


FOUNDATIONS OF CONDUITS. 


433 


ing under Lake Michigan two miles from the shore to the 
lake crib, and underneath the city to the side opposite to 
the shore of the lake. It is 7-0" wide and 7-2" high in the 
clear. The masonry of this tunnel consists of three rings of 
brickwork, the two inner of which have the sides of their 
bricks in radial lines, and the outer having its sides of 
brick at right angles to radial lines. This tunnel was com¬ 
pleted in 1874. 

Fig. 83 is a section of the Boston conduit, commenced in 
1875, to lead an additional supply from Sudbury River to 
the Chestnut Hill reservoir. Its length is sixteen and one- 
lialf miles, its width 9-0", and height 7-8". 

The new Baltimore conduit, as in progress in 1876, is to 
be 36,495 feet in length, entirely in tunnel, extending from 
Gunpowder River to the receiving reservoir. The portions 
lined with masonry are circular in section, of 12 feet clear 
diameter. The inclination is 1 in 5000, and the anticipated 
capacity about 170,000,000 gallons per 24 hours. 

The Cochituate conduit of the Boston water supply is 
5 feet wide, 6 -4" high, of oviform section, and has an incli¬ 
nation of 3J inches to the mile. Its capacity is 16,500,000 
gallons per 24 hours. 

434. Foundations of Conduits. —The foundations of 
masonry conduits must be positively rigid, since the super¬ 
structures are practically inelastic, and any movement is 
certain to produce rupture. A crack below the water-line 
admits water into the foundation, and tends to soften or 
undermine the foundation, and to further settlement, and 
to additional leakage. So long as the foundation yields, 
the conduit cannot be maintained water-tight, for the set¬ 
tling away of the support at any point results in an undue 
transverse strain upon the shell, and the adhesion of the 
mortar to the masonry is overcome and the work cracks. 

28 


434 


MASONRY CONDUITS. 


435. Conduit Shells. — A perfect shell should have 
considerable tensile strength in the direction of its circum¬ 
ference ; but when a longitudinal crack is produced its 
tensile strength is destroyed at that point, and cannot again 
be fully restored except by rebuilding. 

When the side walls are of rubble masonry they are 
usually lined with a course of brick-work laid in mortar, or 
with a smooth coat of hydraulic cement mortar. The bot¬ 
toms are frequently lined with a nearly flat invert arch of 
brick. 

All the materials and workmanship entering into this 
class of structures should be of superior quality. 

436. Ventilation of Conduits.— Conduits of form and 
construction similar to those above illustrated are usually 
proportioned so that they are capable of delivering the max¬ 
imum volume of water required when flowing about two- 
thirds full. Provision is then made for the free circulation 
of a stratum of air over the water surface and beneath the 
covering arch. 

Fig. 90. Fig. 91. 




Figs. 90 and 91 illustrate the form of ventilating shaft 
and cover used upon the New Bedford, Mass., conduit. 




































































































































CONDUITS UNDER PRESSURE 


435 


These shafts may be used also for man-hole shafts, which 
are required at frequent intervals for inspection and care of 
the conduit. 


Fig. 92. 



437. Conduits under Pressure.— Fig. 92 illustrates a 
conduit of locked bricks, designed by the writer to convey 
water under pressure. The specially moulded bricks are 
eight inches long and eight inches wide and two and one- 
lialf inches thick. They have upon one side a mortise six 
inches long, four and one-quarter inches wide, and one-lialf 
inch deep, and upon the opposite side two tenons, each 
matching in form a half mortise. When the bricks are laid 










































436 


MASONRY CONDUITS. 


in the shell the tenons at the adjoining ends of two bricks 
fill the mortise in the brick over which the joint breaks. 

In brick conduits as usually constructed the bricks have 
their greatest length in a longitudinal direction, but here the 
length is in circumferential direction. The object here is to 
utilize to the fullest extent the tensile bonding strength of 
the masonry, and then to reinforce this strength by inter¬ 
locking the bricks themselves. The conduit cannot be rup¬ 
tured by pressure of water without shearing off numerous 
tenons in addition to overcoming the cohesive strength of 
the masonry. 

This system permits of vertical undulations in the grade 
of the conduit within moderate limits, and reduces mate¬ 
rially the amount of lift of the conduit required upon em¬ 
bankments. 

Upon long conduits it permits the insertion of stop-gates 
and the examination and repair of any one section while 
the other sections remain full of water. Also when of 
a given sectional area and flowing full, and delivering 
to a pump-well or directly into distribution-pipes a given 
volume of water, it transfers more of the pressure due 
to the head than the usual form of construction of like 
sectional area, and thus reduces the lift of the pump or 
increases the head upon the distribution. This is more 
especially the case when the consumption is less than the 
maximum. 

488. Protection from Frost.— The masonry of con¬ 
duits must be fully protected from frost, or its cement 
mortar will be seriously disintegrated by the freezing and 
expansion of the water filling its pores. The frost coverings 
are usually earthen embankments, of height above the top 
of the masonry equal to the greatest depth to which frost 
penetrates in the given locality. The level breadth of the 


MASONRY TO BE SELF-SUSTAINING. ' 437 

top of the embankment should equal the breadth of the 
conduit, and the side slopes be not less than 1-| to 1. 

439. Masonry to be Self-sustaining*. —When the 
conduit is in part or wholly above ground surface, its ma¬ 
sonry should be self-sustaining under the maximum pres¬ 
sure, independent of any support that may be expected 
from the embanked earth. The winds of winter generally 
clear the embankments very effectually of their snow cover¬ 
ings, and leave them exposed to the most intense action 
of frost. 

In periods of most excessive cold weather the entire em¬ 
bankment may be frozen into a solid arch, and by expan¬ 
sion rise appreciably clear of the masonry, and possibly 
exert some adhesive pull upon the fiances of the arch. If 
the conduit is then under full pressure, and not wholly 
independent of earth support, a change of form, and rup¬ 
ture of the arch may result. 

Each quadrant of the covering arch, above its springing 
line, exerts a horizontal thrust at the springing line as indi¬ 
cated in Fig. 92 by the shorter arrow, and the water pres¬ 
sure exerts an additional horizontal thrust, as indicated by 
the lower arrow in Fig. 92. When the conduit is just even 
full, the point of mean intensity of this latter pressure is at 
one-third the height from the bottom of the conduit. 

The amount of horizontal pressure upon each side in 
each unit of length is equal to the vertical projection of the 
submerged portion of that side, per unit of length into 
the vertical depth from free water surface, of the centre of 
gravity of the submerged surface, into the weight of one 
cubic foot of water; the depths being in feet, and weight 
and pressure in pounds. 

The product of weight of backing masonry at any given 
depth below the crown of the arch into its coefficient of 




438 MASONRY CONDUITS. 

friction, should be greater than the sum of thrusts at that 
depth, and for a safe margin to insure frictional stability 
should be equal to double the sum of thrusts. 

The backing masonry is liable to receive some pull from 

the embankment, if one 
side of the embankment 
settles or slides, but if the 
foundations of the sides of 
the embankments are rea¬ 
sonably firm, the earth at 
the sides of the backings 
may be assumed capable 
of neutralizing the thrusts 
due to the weight of cover¬ 
ing earth upon the liances 
of the arch. 

440. A Concrete Conduit. —The use of hydraulic 
concrete, or beton , is at present being more generally intro¬ 
duced into American hydraulic constructions, in those 
localities where good quarried stones are not readily and 
cheaply accessible, than has been practiced in years past. 

Fig. 93 is introduced here as a matter of especial interest, 
since it illustrates the form of a conduit constructed entirely 
of beton, in the new Yanne water supply for the city of 
Paris. This conduit is two meters (6.56 feet) in diameter. 

The beton agglomere of this conduit is a very superior 
quality of hydraulic concrete, which has resulted from the 
experiments and researches of M. Francois Coignet, of Paris. 

Gen. Q. A. Gillmore has described* in Professional 
Papers, Corps of Engineers, U. S. Army, No. 19, the mate¬ 
rials, compositions, manipulations, and properties of this 


Fig. 93. 



* Report on Beton Agglomere, or Coignet Beton. Washington, 1871. 













I 


EXAMPLE OF CONDUIT UNDER HEAVY PRESSURE. 439 

beton in a masterly manner, and lias given several plates 
illustrating some of the magnificent monolithic aqueducts 
of concrete, spanning valleys and quicksands, in the great 
forest of Fontainebleau, on the line of the Vanne conduit, 
between La Vanne River and the city of Paris. 

441. Example of Conduit under Heavy Pressure. 
—The details of the Penstock, leading water from the canal 
above referred to (§ 382), to the Manchester, N. H., turbines 
and pumps, are shown in Fig. 94. 

This penstock is six hundred feet long, and six feet clear 
internal diameter. Its axis at the upper end is under 
twelve feet head of water, and at the lower end under thirty- 
eight feet head of water. It was constructed, in place, in a 
trench averaging thirteen feet deep. The staves, which are 
of southern pitch-pine, 4 inches thick, w T ere machine-dressed 
to radial lines, and laid so that each stave breaks joint at its 
end at a distance from the ends of the adjoining staves, after 
the usual manner of laying long floors. The end-joints 
where each two staves abut are closed by a plate of flat 
iron, one inch wide, let into saw-kerfs cut in the ends of the 
staves at right angles to radius. Thus a continuous cylin¬ 
der is formed, except at the two points where changes of 
grade occur. The hoops are of 2|- x ^-inch rolled iron, each 
made in two sections with clamping bolts, and they are 
placed at average distances of eighteen inches between 
centres. 

Its capacity of delivery is sixty-five million gallons in 
twenty-four hours, with velocity of flow not exceeding four 
feet per second.* It was completed in the spring of 1874, 
and has since been in successful use, requiring no repairs. 
It lies in a ground naturally moist, and sufficiently satu- 

* This penstock is more fully described in a paper read before the Ameri¬ 
can Society of Civil Engineers in January, 1877. Vide Trans., March, 1877. 




VERTICAL SECTION 



CYLINDRICAL WOODEN PENSTOCK. 























































































































































































































MEAN RADII OF CONDUITS. 


441 


rated to fully protect the wood-work from the atmospheric 
gases. 

The city of Toronto, Canada, has just completed a con¬ 
duit of wood, which conveys water under pressure from the 
filtering gallery on an island in Lake Ontario, opposite to 
the city, about 7,000 feet, to the pumping-station on the 
main land. The internal diameter of this conduit is 4 feet. 

442. Mean Radii of Conduits. —In the formula of 
flow for open canals (§ 323), the influence of the air pe¬ 
rimeter is taken into consideration in establishing the value 

„ ,, x 7 7 . 7/7 sectional area, S 7 

of the hydraulic mean depth, r =-■ *—, and a 

* contour, C 

fractional portion of the air perimeter, equal to its propor¬ 
tional resistance, is added to the solid wet perimeter. 

It is more especially necessary that the resistance of the 
air perimeter be recognized in conduits partially full. As 
the depth of water increases above half-depth, the influence 
of the confined air section is, apparently, inversely as the 
mean hydraulic radius of the stream. 

If we compute, for circular conduits, values of r, as equal 

to —t— ffv ' 1 - Qn . — T —, we have at o depth, r — 0d\ at one- 
wet solid perimeter 

fourth depth, r — .14734 d ; at one-half depth, r = .2 5d ; at 
three-fourths depth, r — .30133^; and at full depth, r = .2 5d. 
This series gives a maximum value of r at about eight-tenths 
depth and a decrease in its value from thence to full. 

The relative discharging powers, in volume, of a circular 
conduit, with different depths of water, are as the product 

S a/—, when S is the sectional area of the stream ; r, the 
V m 

mean hydraulic radius ; and m , a coefficient. 

If for a given series of depths, in the same conduit, we 
compute its series of volumes of discharge, neglecting the 




442 


MASONRY CONDUITS. 


influence of the air perimeter, we arrive at the paradoxical 
result that when the depth is eighty-eight hundredths of 
full the volume flowing is ten per cent, greater than when 
the conduit is full. This theoretical result has misled sev¬ 
eral liydraulicians who have written upon the subject. 

With a true value of r, the discharge has some ratio of 
increase so long as sectional area of column of water in a 
circular conduit increases; but the maximum capacity of 
discharge of a conduit is very nearly reached when it is 
seven-eighths full. 


TAB LE No. 90. 

Hydraulic Mean Radii for Circular Conduits, Part Full. 

(.Expressed in decimal parts of the diameter .) 


, Ratio of Full Depth. 

o I .1 I .2 | .25 I .3 I .4 I .5 I .55 I .6 I .65 I .7 I .75 I .8 I .85 I .875 I .9 I .95 I Full. 


Hydraulic Mean Radii, in Ratio of Diameter. 
o | .058I • 110 1 .136I .157 1 .200 1 .235 | .250I .263I .272I .275.1.278 1 .277 1 .273 1 .270I .265 1 .260I .250 


443. Formulas of Flow, for Conduits.—Rankine’s 
formula* for loss of head in an open conduit is, 



ml v 2 
r 2 g' 



from which, by transposition, we have the equation of 
velocity, 


v = 


%gh"r \\ _ 
ml \ — 




For value of the coefficient m he adopts Weisbacli’s for¬ 
mula, viz.: 


/ 


m = .0074 + 


.00028 

v 


* Civil Engineering, p. 678. London, 1872. 











FORMULAS OF FLOW, FOR CONDUITS. 


443 


This formula for m gives a constant value to m, while v 
remains constant, even though r varies. Experiment shows 
that the variable r exerts a very appreciable influence upon 
the value of the coefficient m, when 





It is unfortunate that data for the construction of a table 
of m for conduits, not under pressure, is so scanty. Their 
values for brick conduits, or brick linings for a given series 
of r, evidenly lie somewhere between the values of m for 
smooth pipes under pressure, and the values of m for 
straight open channels in earth. 

The following column of values for the given series of r. 
are suggested merely as approximate mean values for 
smooth conduits three-quarters full, and are placed between 
columns of values of m for smooth pipes under pressure, 
and for straight open channels in earth for convenience of 
ready comparison. 

They are applicable to the formulas, for conduits : 



in which 

v = velocity of flow, in feet per second. 

* 

r — hydraulic mean radius. 
i = sine of inclination of water surface. 
h" — vertical head lost in given length, in feet 
l = given length, in feet. 







444 


MASONRY CONDUITS. 


TABLE No. 9 0 a . 

Coefficients for Smooth Conduits, Three-Quarters Full. 

{For a mean velocity of about 2.5 feet per second.) 


Hydraulic mean radii 
r in feet. 

Coefficient m for 
smooth pipes, under 
pressure. 

Coefficient m for 
smooth conduits, 

- 2 £ ri 

Z / 3 

Coefficient m for open 
channels in earth. 

I 

.00380 

.OIOO 

. 0298 

1-25 

.OO342 

.0084 

.0260 

1 . 5 ° 

.OO325 

.0071 

.0234 

1 • 75 

.00300 

.0063 

.0212 

2 

.00281 

.0057 

• OI 97 

2.25 

.OO27 

•°°53 

.0183 

2.50 

.002 6 

. 0050 

.0172 

2 -75 


.0048 

.0161 

3 


.0046 

• OI 53 

3-25 


.0045 

.0145 

3 - 5 ° 


.0044 • 

: - OI 3 8 

3-75 


.0042 

.0132 

4 


.0040 

.0127 


A mean velocity of flow of about two and one-half feet 
per second is usually preferred in smooth conduits and 
supply mains, when local circumstances permit the inclina¬ 
tion and sectional area to be adapted to this end. Less 
velocities, in conduits of three feet or more diameter, per¬ 
mits the waters to deposit the sediments they have in sus¬ 
pension. 

444. Table ol Conduit Data. — The following table 
gives such data as is at present obtainable respecting some 
of the well-known conduits of masonry : 






















1 



''SilW'W 


•««»> 



c- 

o 

© 

£ 

o 

E-« 


»o 

rt> 

Q? 

©*_L 


:i 


j 


SECTIONS OF CROTON NEW AQUEDUCT, 1886. 





















































































































CONDUIT DATA. 


445 


TABLE No. 9 1. 


Conduit Data. 


Locality. 

■ 4 —» 

is 

- 4 —» 

►r* 

t-H 

Depth of 
Water. 

r . 

i . 

V 

per 

sec. 

m . 

Daily de¬ 
livery at 
given 
depth. 

Total 

daily 

capacity. 

Cochituate, Boston. 

Feet . 

Feet . 

6-333 

8.458 

9 

8.667 

7.667 
12 

Feet . 

6 -333 

6.083 

3-465 

5-oo 

1.417 

2.3415 

1-8735 

2.5241 

2.4588 

3.0000 

2.5253 

. 0000496 
.00021 

Feet . 

1.0 

. 00.4 C 2 

U . S . gal . 
16,398,980 
59,340,243 

27 , 559 i 3 6 4 

48,205,128 

86,300,000 

U . S . gal . 
16,500,000 
100,000,000 

Croton, New York. 

7417 

9 

10 

2.218 

• 006435 
.00505 
.00645 

Washington Aq., D. C... 
Brooklyn, L. I. 

.00015 

1.893 

1.588 

3.029 

100,000,000 
70,000,000 
100,000,000 
170,000,000 
60 000,000 
52,000,000 

Sudbury, Boston. 

Q 


Baltimore. 

12 

D j 

12 . OO 



Loch Katrine, Glasgow.. 
Canal of Isabel 11 , Madrid 
Vienna. 

8 

7.0522 

5.667 

6.6 

8 

9.184 
6.0 

6.85 

.0001578 

1.7126 
• • •. 

.00876 

60,000,000 

• 

Vanne, Paris. 

6.6 

5.00 


.0001 




23,500,000 

5,500,000 

Dhuis, “ . 

2 . 2 

Q. ^ 


. 0001 




Pont du Gard, Nimes.... 
Pont Pyla, Lyons. 

4.00 

!-833 

3-167 


3-333 

i -«33 

2.167 

.... 

.0004 
.00166 

2 

2.95 

2.783 



Metz . 

.... 


.001 

. 0004 




Arcueil. 

... . 





Roquencourt, Versailles . 
Caserte. Naples. 

3-925 


2.583 

.... 

.0003 

.0002 

.0003 




.... 

Montpellier. 

I 


o -5 


* j 

. 716 












From data of flow* in the Sudbury Conduit of the Boston 
water works (Fig. 83, p. 431) the following table of values of 
m for a series of r has been computed, in which 

m=(2g7'i)^rTr=2g+-C'\ and C= V2g-±m. 


TABLE No. 91a. 


r 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

o -7 

0.8 

0.9 

1.0 

I. I 

1.2 

i-3 

i-4 

->n 

.00690 

.00587 

•00533 

•00497 

.00471 

.00451 

•00435 

.00421 

.00416 

.00399 

.00392 

.OO382 

•00375 

.00363 

c 

96-3 

104.7 

109.9 

113.8 

116.9 

“ 9-4 

121.7 

123.6 

125.4 

127.0 

128.5 

129.8 

131-1 

132.2 

r 

1-5 

1.6 

1.7 

1.8 

1.9 

2.0 

2.1 

2.2 

2.3 

2.4 

2.5 

2.6 

2-7 

2.8 

m 

.00362 

00357 

•00352 

•00347 

.00342 

.00339 

•00336 

.00332 

.00330 

.00328 

•00327 

.00326 

.00325 

.00324 

c 

133-3 

134-4 

135.3 

136.2 

x 37 • 1 

137-8 

138-5 

I39-I 

139-6 

140.0 

140.4 

140.6 

140.8 

141.0 


These coefficients for the given values of r may be used 
in the formulas for velocity, Vri , and v=C Vri. 


Resident engineer Fteley found v = 127 r ,G2 I> to repre¬ 
sent well the results of experiments up to the value 1.6 
for r. He found also that a liquid cement wash on the 
interior of the brick conduit increased the flow about two 
per cent., while in the unlined rock tunnel of similar section 
the flow decreased about forty per cent. 

The low values of m are an indication that the short 
section of conduit in which the experiments were conducted 
was very smooth. 


* Descriptive Report of Additional Supply of Water to Boston, from Sud¬ 
bury River, by Alphonse Fteley, resident Engineer.—Boston, 1882. 






















































































CHAPTER XXI. 

MAINS AND DISTRIBUTION PIPES. 


445. Static Pressures in Pipes. —Passing from the 
consideration of masonry conduits to that of pipes with 
tough metal shells, the pressure strains and the capabilities 
of resistance of the pipe metals to these strains, first de¬ 
mands our attention. 

The theoretical relations of thickness to pressure are so 
simple that we may easily adapt any tough metal pipe to 
withstand any practical static head pressure, however great. 

By the term static 'pressure , we indicate the full pressure 
due to the head of water, while standing at rest. 

The unit of pressure area is commonly taken as one 

square inch, and this is the area used 
herein for the unit. 

The pressure p upon the unit of 
area a x of a conduit or water-pipe, is 
equal to the product of the given area 
into the vertical height h of the surface 
of water above the centre of gravity of 
the given area, into the weight w of 
one cubic foot of water (= 62.5 lbs.) 
divided by 144. 


Fig. 95 . 




a x x h x w 

144 


.434^. 



Let abcef \ Fig. 95, be the internal circumference of a 








Fig. 96a. 




V B0ST0N 

\yv E ,c »7 ,!«■» 


WEIGHT.'yjTu 

LENG T H: 




■ ■■ 


weight: z/5z iia. 
length: ntksiiv. 




FORMS OF PIPE SOCKETS. 











































































































THICKNESS OF SHELL. 


447 


water-pipe, of diameter cl , in inches ; then the total pressure 
P of water upon the circumference is 

P = 3.1416d x .434^. (2) 

The maximum pressure acts upon each point of the cir¬ 
cumference radially outward, tending to tear the shell 
asunder. 

The resultant of the maximum pressure upon any given 
portion of the circumference ab, acts in a radial direction 
ox , through the centre of gravity of the surface ob , and is 
equal to the product of pressure into the projection or trace 
of the surface (/, at right-angles to radius, 

= {(area if) x p\. 

Also the resultant of the maximum pressure upon the 
semi-circumference cbaf is equal to the product of pressure 
into its trace gk, at right-angles to the radial line cutting its 
centre of gravity, 

= {(area glc) x p\. 

The trace of the semi-circumference is also equal to the 
diameter cl , and its resultant equals the product dp. 

Opposed to the resultant ox is an equal resultant of the 
pressure upon the semi-circumference fee. 

These two resultants exert their maximum tensile strain 
upon the pipe-shell at the points c and/. 

446. Thickness of Shell resisting Static Pressure. 
—Let S he the cohesive strength or ultimate tenacity per 
sq. in. of the metal of the shell, and t be the thickness cc l and 
ff x in inches of the shell, then we have for equation of resist¬ 
ance of shell that wiLL/&s£ bcdance the steady static pressure, 

2tS = dp. 

from which we deduce the required thickness of shell: 


( 3 ) 


448 


MAINS AND DISTRIBUTION PIPES. 


dp _rp 
S~ ~S’ 



in which r equals radius in inches, = — 

It is not enough that the shell be able to just sustain the 
steady static pressure, since this pressure may be increased 
by “ water-rams ,” incident to ordinary or extraordinary 
use of the pipe, or the metal may have unseen weaknesses, 
or deteriorate by use. 

The thickness t should therefore be multiplied by a 
coefficient, for safety, equal to 4, 6, 8, or 10 ; or the pressure 
be assumed to be increased 4, 6, 8, or 10 times, or the 
tenacity of the metal be taken at .1, .2, .8, or .4 of its test 
value; in which case the equation of t may take the form, 



10 pr 


or 




If F is the factor of safety, then 

t = ^ X F and F = (6) 
8 pr 

• , 

This factor will vary with the conditions of use and 
materials, as in water pipes, inclosed stand-pipes, vented 
penstocks, or boilers, and must include weaknesses due to 
manufacture, as in riveted joints, etc. Vide rivets , Chap. 
XXV. 

The irressure due to a given head II of water is greater 
within a pipe when the water is at rest, than when the cur¬ 
rent is flowing through the pipe at a steady rate, for when 
the current is moving, a portion of the force of gravity is 
consumed in producing that motion, and in balancing fric¬ 
tions. 

When a pipe has a stop-valve at its outflow, or in its 
line, the pressure p , used in its formula of thickness t , for 






WATER-RAM. 


449 


any point above the valve, should be the static pressure of 
the water at rest. 

447. Water-ram.—If any valve in a line or system of 
water-pipes can be suddenly closed while the water is flow¬ 
ing freely under jDressure, such sudden closing of the valve 
will produce a strain upon the pipes far greater than that 
due to the static head of water, and in addition thereto. 

For illustration, let the diameter, d x = 1 ft., length, l = 
5280 ft., and velocity of flow, v — 5 ft. per second. Then 
the accumulated energy, M, in the column of water, due to 
its weight, w x (= 62.5 lbs.), and velocity, is 


M = (.7854 ct\ x Wi x l) x ^ = 100614.45 ft. lbs. 

J 2g 2g 

W = 259182 lbs. and the equivalent head 7i = .3882 foot. A 
body falling freely through .3882 foot height would consume 
time equal to (27^ -r- v), or (v g) — .15524 second. M is 
therefore equivalent to a pressing force of .15524 W = 
40245.78 lbs. acting one second through five feet with a 
mean velocity of two and one-half feet. 

Since the area of the valve in square inches is .7854 d* x 
144, the pressure p x in lbs. per square inch on valve and 
adjacent pipe wall is, when the column is uniformly checked, 
40245.78 lbs.^-(.785467! 2 x 144) = 355 lbs., and increased if the 
checking is not uniform. 


Pi = 


Wv^-g 


.7854 d? x 144 


for a minimum uniform strain of 


ram, and the equivalent static head in feet = p x -f- .433. 
Accumulations of air in the pipe summits will help to 
cushion the force of ram and modify the strain behind them. 

ISTo system of distribution-pipes should be fitted with 
stop-valves of rapid action, lest the pipes be constantly 
in danger of destruction by “ water-rams .” 

Genieys made allowance, in the old water-pipes of Paris, 
for water-rams, of force equal to static heads of 500 feet, 




450 


MAINS AND DISTRIBUTION-PIPES. 


but he used on liis smaller mains plug-valves that might be 
very rapidly closed. 

With proper stop and hydrant valves, it is not probable 
that the momentum strain will exceed that due to a steady 
static head of 200 or 225 feet, but it is liable to be great in 
pipes under low static heads as well as in pipes under great 
heads, and it is in either case in addition to the static head. 
The momentum strain must be fully allowed for, whether 
the head be ten feet or three hundred feet. 

448. Formulas of Thickness for Ductile Pipes.— 
Ordinarily, for ductile pipes, such as lead, brass, wielded 
iron, etc., an allowance of from 200 to 300 feet head is made 
for the momentum strain, and the tenacity of the material 
is taken at .25 or .3 of its ultimate resistance S , in which 
case the formula for thickness of ductile pipes , subject to 
water-ram, may take the form, 

' _ (h + 230 ft.) no _ (Ji + 230 )dw _ ( 'll + 230)dw , 

1 ~ (.25 S) x 144 “ (JS)~xlU - 72S) 5 W 


in which li is the head of water, in feet. 

w “ “ weight of one cubic foot of water, in lbs. 
r “ “ radius of the pipe, in inches. 
d “ “ diameter of the pipe, in inches. 
t u “ thickness of the pipe-shell, in inches. 

S u “ tenacity of the metal, per square inch. 


If we substitute a term of pressure per square inch, p 
(— .4347^), for in the equation for thickness of ductile 
pipes , it becomes 


f _ (P + 100 pounds) r (p + 100) d 
~ . 2 WS ~ 



If the pipes have merely a steady static pressure to sus- 








MOULDING OF PIPES. 


451 


tain, then the term + 100 may be omitted, and the equation, 
with factor of safety equal to 4, takes the simple form, 


pr _ pd 
~ . 25 # ~ 



or with factor of safety equal to 6, 

, _ pr _ pd 
t ~ 36607 # “ 



449. Strengths of Wrought Pipe Metals.—The fol¬ 
lowing values of S give the tenacities of the respective ma¬ 
terials named, in pounds per square inch of section of 
metal , when the metal is of good quality for pipes: 


TAB LE No. 92. 
Tenacities of Wrought Pipe Metals. 



Weight 
per Cu¬ 
bic Inch. 


Pounds. 

Lead. 

.411Q 
.2637 
. IO46 
• 3000 
.3146 
.2607 
.2607 

Rlork tin. 

Glass . 

Brass. 

Copper. 

WroWht-iron, single riveted. 

“ u double “ . 




COEF. 

Coef. 

Coef. 

Coef. 


6 (Jr). 

4 (pr). 

6 (Jd). 

4 (Pd). 

S', in lbs. 

.16667s 1 . 

.25 S. 

• 33333 S. 

• 5 s. 

2,000 

333-33 

500 

666.67 

IOOO 

4,600 

766.66 

1150 

1 533-33 

2300 

9,400 

1566.66 

2350 

3 * 33-33 

4700 

28,000 

4666.66 

7000 

9333-33 

14000 

30,000 

5000 

7500 

I OOOO 

15000 

35 ! 0 ® 0 

5833-33 

8750 

11666.66 

17500 

40,000 

6666.66 

IOOOO 

* 3333-33 

20000 


CAST-IRON PIPES. 

450. Moulding of Pipes.— The successful founding 
of good cast-iron pipes requires no inconsiderable amount 
of skill, such as is acquired only by long practical experi¬ 
ence, and keen, watchful observation. 

The loam and sand of the moulds and cores must be 
carefully selected for the best characteristics of grain, and 






































452 


MAINS AND DISTRIBUTION-PIPES. 


proportioned, combined, and moistened, so that the mix¬ 
ture shall be of the right consistency to form smooth and 
substantial moulds and cores, and be at the same time suf¬ 
ficiently porous to permit the free exit of moisture and 
steam during the process of drying. The moulds must be 
filled and rammed with a care that insures their stability 
during the inflow of the molten metal, and must be dried 
so there will be no further generation of steam during the 
inflow; and yet not be overdried so as to destroy the ad¬ 
hesion among their particles, lest the grains of sand be 
detached and scattered through the casting. The core rop¬ 
ing of straw must be judiciously proportioned in thickness 
for the respective diameters of their finished cores, and must 
be twisted to a firmness that will resist the pressure of the 
molten metal, so that the pipe will be free from swells and 
the proper and uniform thickness of metal will be secured. 
The mixture of the metals and fuel in the cupola must 
be guided by that experience by which is acquired a fore¬ 
knowledge of the degree of tenacity, elasticity, and general 
characteristics of the finished castings. A superior class of 
pipe is produced only when excellent materials are used, 
and when superior workmanship and mechanical appli¬ 
ances give to them accuracy of form and excellence of 
texture. 

451. Casting* of Pipes.—A certain thickness of shell, 
of twelve-foot pipes, cast vertically, is required for each 
diameter of pipe, to insure a perfect filling of the mould 
before the metal chills, or cools, and also to enable the 
]iipes to be safely handled, transported, laid, and tapped. 

In the smaller pipes this thickness is greater than that 
ordinarily required to sustain the static pressure of the 
water. 

The necessary additional thickness, beyond that re- 


THICKNESS OF CAST-IRON PIPES. 


453 


quired to resist the water pressure, decreases as the diam¬ 
eter of the pipe increases. 

There must, therefore, be affixed to the formula of thick¬ 
ness of cast-iron pipes, a term expressing the additional 
thickness required to be given to the pipes beyond that re¬ 
quired to resist the pressure of the water, and this term 
must decrease in value as the diameter increases in value. 

452. Formulas of Thickness of Cast-iron Pipes. 
—The ultimate tenacity of good iron-pipe castings ranges 
from 16,000 to 29,000 pounds per square inch of section of 
metal. Their value of 8, the symbol of tensile strength 
per square inch, is usually taken at 18,000 pounds, and the 
coefficient of safety equal to 10, or the term of tensile resist¬ 
ance is taken equal to .1$, or if an independent term is 
introduced in the formula for the effect of water-ram, the 
coefficient of 8 may be increased to, say .2. 

Assuming that the probable or possible water-ram will 
not produce an additional effect greater than that due to a 
static pressure of 100 pounds per square inch, or head of 
230 feet, then the formula for thickness of cast-iron pipes 
may take the form, 

/ _ (h + 230 )rw , QQq L d \ _ (h + 230 )dw 

(.28) x 144 + \ 100/ - (AS ) x 144^ + 

•333 (l - A). (11) 

in which h is the head of water, in feet. 

io “ weight of one cubic foot of water, in lbs. 
r “ internal radius of the pipe, in inches. 
d “ internal diameter of the pipe, in inches. 
t “ thickness of the pipe shell, in inches. 

8 “ tenacity of the metal, in pounds per sq. in. 

If we substitute a term of pressure per square inch, 





454 


MAINS AND DISTRIBUTION PIPES 


p (== .434/^) for in the above equations for thickness 


of cast-iron pipes, they become, 




( 12 ) 


453. Thicknesses found Graphically.—Since with a 
constant head, pressure, or assumed static strain, the in¬ 
crease of tensile strain upon the shell is proportional with 
the increase of diameter, and also since the decrease of 
additional thickness is proportional with the increase of 
diameter, it is evident that if we compute the thickness of a 
series of pipes, say from 4-inch to 48-incli diameters, for a 
given pressure, by a theoretically correct formula, and then 
plot to scale the results, with diameters as abscissas and. 
thicknesses as ordinates, the extremes of all the ordinates 
will lie in one straight line ; and also, that if the thicknesses 
for the minimum and maximum diameters of the series be 
computed and plotted as ordinates, in the same manner, 
and their extremities be connected by a straight line, the 
intermediate ordinates, or thicknesses for given diameters 
as abscissas, will be given to scale. This method greatly 
facilitates the calculation of thicknesses of a series of 
“ classes” of pipes, and if the ordinates are plotted to large 
scale, gives a close approximation to accuracy. 

454. Table of Thicknesses of Cast-iron Pipes.— 
The following table gives thicknesses of good, tough, and 
elastic cast-iron, with S = 18,000 lbs., for three classes of 
cast-iron pipes, covering the ordinary range of static pres¬ 
sures of public water supplies. 

The thicknesses in the table are based upon the formula, 











THICKNESSES OF CAST-IRON PIPES. 


455 


TABLE No. 93. 

Thicknesses of Cast-iron Pipes. 

(When S = 18000 lbs.) 



CLASS 

A. 

CLASS 

B. 

CLASS 

c. 

Diameter. 

Pressure, 50 lbs. per 
square inch, or less. 
Head, 116 feet. 

Pressure, 100 lbs. per 
square inch. 

Head, 230 feet. 

Pressure, 130 lbs. per 
square inch. 

Head, 300 feet. 


Thicknesses. 

Thicknesses. 

Thicknesses. 

Inches. 

3 

Inches. 

•3 8 5 8 

Ap¬ 

prox. 

in. 

13 

3 2 

Inches. 

• 

.4066 

Ap¬ 

prox. 

in. 

I 3 

3 2 

Inches. 

.419 1 

prox. 

in. 

7 

T¥ 

4 

•4033 

I 3 

3 2 

•43 11 

7 

T¥ 

•4477 

7 

T¥ 

6 

•43 8 3 

7 

T¥ 

.4800 

1 

2 

•5050 

i 

8 

•4734 

1 

2 

.5289 

I 7 

32 

.5622 

T6 

10 

•5 o8 3 

1 

2 

•5777 

19 

T2 

.6194 

5 

¥ 

12 

•5433 

9 

T¥ 

.6266 

5 

¥ 

.6766 

I I 

Ter 

14 

•57 8 3 

I 9 
¥2 

•6755 

I I 

T¥ 

•733 8 

3 

V 

16 

.6166 

5 

¥ 

.7277 

3 

T 

•7944 

13 
T¥ 

18 

.6483 

2 I 

3 2 

•7733 

2 5 

3 2 

•8483 

2 7 

32 

20 

• 68 33 

I I 

T(T 

.8222 

2 7 
3¥ 

•9055 

29 

TT 

22 

•7 i8 3 

23 

3 2 

.8711 

7 

¥ 

.9628 

3 I 
TT 

24 

•7533 

3 

.9200 

I 5 

I 6 

1.0200 

I 

27 

.8058 

13 

T<r 

•9933 

I 

1.1058 

t 3 
r 32 

30 

•8583 

7 

¥ 

1.0666 

I A 

1.1916 

T 3 

33 

.9108 

1 5 
T¥ 

1.1400 

T 5 
*¥2 

I - 2 775 

T 9 
I ¥2 

3 6 

•9633 

3 I 
¥¥ 

1.2133 

T —L 

1 3 2 

1-3633 

T 3 

T ¥ 

40 

i-o333 

T I 

i -3 111 

T 5 

I T¥ 

1.4778 

T I 5 

1 3 2 

44 

1-1033 

J ¥ 

1.4088 

T 13 

1 3 2 

i-59 21 

T 19 
X J2 

48 

1 • 1 733 

I TF 

1.5066 

4 

1.7066 

T I I 

I Ter 


In the following table are given the thicknesses of cast- 
iron pipes, as used by various water departments. 


























I 


456 


MAINS AND DISTRIBUTION PIPES. 


TABLE No- 93a. 

Thicknesses of Cast-iron Pipes, as Used in Several Cities. 


tr. 

tu 

a 

u 

2 


W 

h 

s 

s 

< 

HH 

Q 


6 

8 

8 

io 

12 

12 

*! 

16 

20 

20 

24 

24 

30 

30 

30 

36 

36 

48 


< 

5 

3 

a 

Q 

1 < 

1 a 

a 

a 

0 

& 

a 

a 

0 

S 

w 

h 

Z 

> 

a 

a 

0 

in 

H. 

D 

O 

P 

0 

0 

< 

u 

Cleveland. 

a 

u 

Z 

a 

Q 
>—« 

> 

a 

a 

a 

> 

a 

a 

H 

in 

a 

X 

a 

a 

> 

Pi 

a 

% 

z 

a 

X 

0 

a 

h 

O 

a 

Eh 

Albany. 

a 

a 

a 

D 

< 

■s 

5 

Oh 

a 

£ 

< 

cq 

O 

K 

CQ 

h 

C/l 

3 

0 

a 

Oh 

0 

P 

0 

Pi 

< 

a 

<1 

a 

P 



Head Pressures for which Pipes 

are 

Classed, 

in feet. 


H 5 

250 

IOO 

218 

120 

170 

130 

170 

125 

150 

IOO 

140 

130 

170 

150 

200 

80 

140 

162 

IOO 

144 

200 

ISO! 

1 

; 200 








198 


180 

200 


260 

















Thicknesses 

of Pipe Shells, in 

inches. 




3 


Tff 


1 

¥ 

1 

¥ 

¥ 


__ 

1 

3 

8 

i 

7 

Tff 

.1 


1 8 

* * * 




2 

2 


7 

Tff 

1 

¥ 

Iff 

Tff 

1 7 
¥¥ 

1 

¥ 

¥ + 

1 

¥ 

7 

tg 

5 

8 

1 5 

¥¥ 

¥ 

7 

Tff 

1 

2 

15 

3 ¥ 




n 

9 

Tff 



1 


7 

5 



6. 

1 






2 

2 

8 

8 



8 

2 

7 1 

Tff + 

• • • • 

1 

1 

¥ 

9 

Tff 

1 

¥ 

1 

¥ 

1 

¥ 

1 

2 

7 

ff 

1 7 
¥¥ 

5 

ff 

1 

¥ 

1 

2 

1 

¥ 




21 

¥¥ 

5 1 

8 + 



9 

9 


3 



5 

9 

Tff 






1 D 

1 b 


4 



8 

1 

w 

• • • • 

¥ 

• • • • 

5_ 

ff 

5 

ff 

5 

8 

1 9 
3 ¥ 

• • • • 

3 

¥ 

3 ¥ 

• • • • 

1 

¥ 

5 

8 

• • • 

9 

Tff 

6 

8 

n 

5 

8 

21 

3 2 

8 

¥ 

8 

¥ 

9 

Tff 

19 
¥¥ 

8 

¥ 

5 

ff 

3 

¥ 

9 

Tff 

5 

8 

Tff 




1 3 

Tff 

23 



2 1 

6. 1 

8 T 

I 

15 

1 6 



3 

¥ 

_5 




.1 2 



3 2 




8 

6 

f 

3 

¥ 

13 

Tff 

• • • • 

• • • • 

7 

ff 

8 _i_ 

¥ ‘ 

21 
¥¥ 

11 _ 

Tff 

3 

¥ 

3 

¥ 

3 

¥ 

5 

ff 

3 

¥ 

11 

16 1 








3 

3 

I 

if 



7 

ff 

... ' 

' 







4 

4 


8 




11 
Tff 

3 

1 5 

Tff 

7 

1 8 
Iff 


7 

2 3 


3 

7 

I 

3 



4 

8 


8 

8 8 


4 

8 


4 


4 - 




1 

15 1 

16 + 



17 


1 

T 5 

Uff 




7 ! 







3 2 






8 


7 

ff 





7 1 

ff + 

13 

Iff 

13 

3 

¥ 

3 

I 



15 |, 






1 b 

4 




ig - 








1 5 

1 6 

15 1 

Tff + 

I 

1 




T 














1 16 

1 

Iff 

iA 

T 1 


if 

19 

Tff + 

7 





I * 

r 6 


8 2 


8 

3 2 

8 








T ^ 

iff 

1 4 



1 

Iff 






i K 




4 









1 iff. 








I Tff 

T 5 

i| 





/• 








16 

16 







1 


ij- 

ii + 


I Tff 

1 




if 

1 


L 



8 






8 








if 



if 







1 /• 





8 



4 









i* 


r_ 5 _ 

if 












4 


16 

8 












</> 

a 

x 

u 

z 


K 

a 

H 

a 

3 

< 


4 

6 

6 

8 

8 


455. Table of Equivalent Fractional Expressions. 

—The following tables of equivalent expressions for fractions 
of an inch and of a foot, may facilitate pipe calculations: 










































































































CAST-IRON PIPE JOINTS. 


457 


TABLE No. 94. 

Parts of an Inch and a Foot, expressed Decimally. 


Inches. 

Equivalent 
Dec. part of 
an inch. 

Equivalent 
Dec. part of 
a foot. 

I-32 

•03125 

.002604 

l-l6 

.06250 

.005208 

3-32 

•09375 

.007812 

i-8 

.12500 

.OIO416 

5-32 

.15625 

.OIO420 

3-16 

.18750 

.015625 

7-32 

.21875 

.018229 

1-4 

.25000 

.020833 

9-32 

.28125 

•023437 

5-16 

•31250 

.026041 

n-32 

•34375 

.028645 

3-8 

• 375 oo 

.031250 

13-32 

.40625 

.033854 

7-16 

•43750 

.036458 

15-32 

.46875 

.039062 

1-2 

.50000 

.041666 

17-32 

•53125 

.044270 

9-16 

.56250 

.046875 

19-32 

•59375 

.049479 

5-8 

.62500 

.052083 

21-32 

.65625 

.054607 

n-16 

.68750 

.057291 

23-32 

•71875 

•059895 

3-4 

.75000 

.062500 

25-32 

.78125 

.065104 

13-16 

.81250 

.067708 

27-32 

.84375 

.070312 

7-8 

.87500 

.072916 

29-32 

.90625 

.075520 

15-16 

•93750 

.078125 

31-32 

.96875 

.080729 

1 

1. 

•083333 


Inches. 

Equivalent 
Dec. parts of 

Dec. parts 
of a foot. 

Equiv. inches 
and 32d pts., 


a foot. 

nearly. 

I 

•0833 

. I 

T 3 

I T^ 

2 

. 1667 

.2 

2^ 

■^8 

3 

.2500 

•3 

a l 9 

3 3^ 

4 

•3333 

•4 

4#f 

5 

.4167 

•5 

6 

6 

.5000 

.6 

1 3 
/Te* 

7 

•5833 1 

•7 

8 3 - 

°8 

8 

.6667 

.8 

9 Hr 

9 

• 75 oo 

•9 

I0 ff 

10 

•8333 

1.0 

12 

11 

.9167 



12 

1.0000 




45G. Cast-Iron Pipe Joints.—According to Crecy,* 
cast-iron pipes were first generally adopted in London very 
near the close of the last century. The great fire destroyed 
many of the lead mains in that city. These were in part 
replaced by wood pipes, but when water-closets were intro¬ 
duced and more pressure was demanded, the renewals were 
afterward wholly of iron. 


* Encyclopedia of Civil Engineering, p. 549. London, 1865. 






































458 


MAINS AND DISTRIBUTION-PIPES. 


The earliest pipes had flanged joints with a packing ring 
of leather, and were bolted together. These were two and 
one-half feet in length. Those first generally used by the 
New River Company were somewhat longer, and were 
screwed rigidly together at the joints. This prevented 
their free expansion* and contraction, with varying temper¬ 
atures of water and earth, rendering them troublesome in 
winter, when they were frequently ruptured. Cylindrical 
socket-joints were then substituted. These were accurately 
turned in a lathe, to a slightly conical form, and, being 
luted with a little whiting and tallow, were driven together. 

The length of the pipes w T as subsequently increased to 
nine feet, and a hub and spigot-joint formed, adapted first 
to a joint packing of deal wedges, and afterward to a pack¬ 
ing of lead. 

The hub and spigot-joint, with various slight modifica¬ 
tions, has been generally adopted in the British and con¬ 
tinental pipe systems, for both water and gas pipes; but 
the turned joint has by no means been entirely superseded 
in European practice. 

A variety of the forms given to the turned joint are illus¬ 
trated and commented upon in a paper f recently read by 
Mr. Downie in Edinburgh. The illustrations include turned 
joints used in Glasgow, Launceston, Dundee, Flyde, Liver¬ 
pool, Trieste, Sydney, Hobart Town, and Hamilton (Canada) 
water-works, and in the Buenos Ayres gas-works. These 
joints were also used by Mr. George H. Norman, the well- 
known American contractor for water and gas works, in 
gas works constructed by him in Cuba. 


* M. Girard found that the lineal expansion of cast-iron pipes, when free 
and in the open air was .000036 of an inch for each additional degree of Fah¬ 
renheit. Rankine gives .0000733 inch per foot per degree, 
f Proceedings Inst. E. S., vol. vii, p. 16. 




DIMENSIONS OF PIPE-JOINTS. 


459 


The turned joint has not as yet been adopted in the 
pipe systems in the United States; but in the new water- 
work of Ottawa, Canada, completed in 1875 under the direc¬ 
tion of Tlios. C. Keefer, C.E., they were very generally used. 

The depths of hub and of lead packing in the early Eng¬ 
lish and Scotch pipes, and in fact in the first pipes used in 
connection with the Fairmount, Croton, and Washington 
aqueducts, exceeded greatly the depths at present used. 

The pine-log water-pipes of Philadelphia had been gen¬ 
erally replaced by cast-iron pipes as early as about 1819. 
The forms of hubs and spigots then used, as designed by 
Mr. Graffe, Sr., were v.ery similar to those now used, ex¬ 
cept that the hubs had somewhat greater depth. The 
lengths of the pipes were nine feet, and other dimensions as 
in the following table, from data in the “Journal of the 
Franklin Institute” : 

Diameter of pipe, in inches. 3 

Thickness of shell. f 

Depth of hub. 3 | 

It is observed that the set, by which the lead is com¬ 
pacted in the joint, acts upon the lead, ordinarily only to a 
depth of from one to one and one-quarter inches. The lead 
beyond the action of the set is of but little practical value, 
and there is no advantage in giving the hemp packing an 
excessive depth. 

Deep joints run solid with lead often give to the line of 
pipes such rigidity that it cannot accommodate itself to the 
unevenness of its bearings and weight of backfilling, espe¬ 
cially in ledge cuttings, and rupture results. 

When trenches are too wet to admit of pouring the lead 
successfully, small, soft lead pipe may be pressed into the 
joint and faithfully set up with good effect. 

457. Dimensions of Pipe-joints.— Fig. 96 is a re- 


4 

6 

8 

IO 

12 

16 

7 

7 

i 

i 

9 

5 

16- 

T6 


2 

Tl> 

8 

4 

4| 

5 

5 


6 












460 


MAINS AND DISTRIBUTION-PIPES. 


Fig. 96. 



duced section of a bell and spigot of a 12-inch diameter 
pipe. Dimensions of cast-iron pipe socket-joints for diam¬ 
eters from 4-incli to 48-inch, corresponding to the letters in 
the sketch, are given in the following table (No. 95), and 
like data are given for flange-joints in the next succeeding 
table, No. 96. 

The weight of flanged pipes, per lineal foot, exclusive of 
weight of flanges, which is given in Table No. 96, may be 
computed by the following formula (vide § 461) : 

w = 9.817 (cl + t)t (13) 

458. Templets for Bolt Holes. —A sheet-metal tem¬ 
plet for marking centres of bolt holes on flanges should be 
laid out and pricked with the nicest accuracy, and have its 
face side and one hole conspicuously marked. 

On special castings intended for fixed positions the tem¬ 
plet should be placed upon the flange so that the centre of 
the marked hole shall fix the position of one bolt hole ex¬ 
actly over the centre of the bore of the pipe when the pipe 
shall be placed in position, then the bolt holes of abutting 
flanges will match with uniformity. 












DIMENSIONS OF PIPES 


461 


TABLE No. 93. 

Dimensions of Cast-iron Water-pipes. (Fig. 96 .) 


(Thickness of shell is herein proportioned for ioo lbs. static pressure.) 


<u 

<D 

S 

d 

Length over all. 

Thickness 
of shell. 

Depth of 
hub. 

Joint room. 












Q 

ab 

bq 

be 



ce 

eg 

ef 

fP 

M 

km 

mn 

lio 

qj 

in. 

4 

/ // 

12-3 

// 

tV 

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3 

rt 

5 

1 ¥ 

// 

if 

// 

if 

/t 

I 8 

ft 

1 

¥ 

it 

3 

x<r 

/f 

3 

¥ 

tr 

1 

¥ 

tt 

5 

X¥ 

If 

3 

¥ 

/t 

7 

¥ 

// 

2 

6 

12-3 

1 

3 

5 

1 6 

if 

if 

If 

1 

¥ 

3 

X¥ 

3 

¥ 

1 

¥ 

5 

T¥ 

3 

¥ 

I 

2 

8 

12-3 

1 7 
¥¥ 

3 

5 

T¥ 

if 

if 

If 

1 

2 

3 

16 

3 

¥ 

1 

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T 5 ¥ 

3 

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if 

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10 

12-3 

1 9 
32 

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if 

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12 

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to 

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5 

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12-31 

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if 

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1 

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16 

7 

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1 

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T6 

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16 

i2-3i 

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3f 

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rs 

■*•8 

lT6 

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5 

l¥ 

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12-31 

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5 

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20 

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if 

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2 ¥ 

22 

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If 

2 

4 





















































462 


MAINS AND DISTRIBUTION-PIPES. 


TABLE No. 96. 

Flange Data of Flanged Cast-iron Pipes. 


Diam. 

of 

bore 

of 

pipe. 

Diameter 

of 

flange. 

Thick¬ 
ness of 
flange. 

Approx, 
weight 
of one 
flange. 

No. of 
bolts.* 

Diam. 

of 

bolts. 

Diameter 
of circle of 
bolts. 

Distance 
between 
centres of 
bolts. 

Com¬ 
mon 
diam. 
of valve 
flanges. 

Inches. 

Inches. 

Inches. 

Pounds. 


Inches. 

Decimal 

inches. 

Decimal 

inches. 

Inches . 

3 

61 

11 

T7T 

3-45 

8 

7 

T¥ 

5-6 

2.199 

8 

4 

7i 

3 

¥ 

6.64 

10 

1 

2 

6.7 

2.IO5 

9 

6 

10 

13 

T<T 

8.56 

10 

9 

T¥ 

8.9 

2.796 

11 

8 

I2f 

13 

T5" 

11.98 

12 

5 

■S' 

II.I 

2.906 

*3 

IO 

J 4f 

7 

¥ 

16.5 

14 

3 

¥ 

*3*3 

2*985 : 

16 

12 

17 

I 5 
T¥ 

, 22 *3 

14 

3 

¥ 

^•S 

3*478 

18 

14 

19* 

I 

28.6 

16 

3 

¥ 

1 7*75 

3-485 

20 

16 

2 if 


36.8 

18 

3 

¥ 

20.0 

3-49 1 

22 

18 

2 3w 

I ¥ 

45-5 

20 

3 

¥ 

22.2 

3-487 

24 

20 

26J 

I A 

56-9 

20 

3 

¥ 

24.4 

3*833 

26} 

22 

28J 

4 

62.8 

22 

3 

¥ 

26.5 

3-784 

28J 

24 

3°f 


65-4 

24 

7 

"S' 

28.6 

3*744 | 

3°¥ 

27 

33f 

T 5 

I T5‘ 

80.8 

26 

7 

¥ 

3 r *8 

3.842 

33 r 

3° 

36J 

I I 

95-9 

28 

7 

¥ 

35-° 

3*9 2 7 

365- 

33 

40 

4 

117 

3° 

7 

¥ 

38. 1 

3*99° ! 

40 

3 6 

432 


143 

3 2 

7 

¥ 

41.6 

4.084 

43 ¥ 

40 

47f 

T 5 

1 S' 

l60 

34 

7 

¥ 

45-75 

4.227 

47i 

44 

5 1 ! 

*¥ 

J 97 

36 

7 

¥ 

50.0 

4*363 

5 X ¥ 

48 

56 

i* 

224 

40 

7 

* 

54-i 

4.249 

56 


* Tlie number of bolts given in the table may be decreased when the 
water pressures and transverse strains upon the bolts are light. 


OC|C/i 









































FLEXIBLE PIPE-JOINT. 


463 


If an even number of bolts are used, then there will be 
a bolt vertically over and under the centre of the bore of 
the pipe. 

If the templet is not very exactly spaced the face side 
should be placed against one flange with the marked hole 
at top, and the back against the other abutting flange with 
same hole at top ; otherwise the bolt holes may not exactly 
match. 

459. Flexible Pipe-Joint .—It is sometimes necessary 
to take a main or sub-main across a broad, deep stream or 


Fig. 97. 



estuary, or arm of a lake, where it is both difficult and 
expensive to coffer a pipe course so as to make the usual 
form of rigid joint. Different forms of ball and socket 
































464 


MAINS AND D1STRIBUTIPN-PIPES. 


flexible joints have been adopted for such cases, which 
allow the pipes to be joined and the joints completed above 
the water surface, and the pipe then to be lowered into 
its bed. 

Fig. 97 illustrates the form of joint designed by the 
writer for a twenty-four inch pipe, which is especially 
adapted to large-size pipe-joints. It is a modification of the 
Glasgow “ universal joint.” 

The difficulty of making the back part of the lead-pack¬ 
ing of the joint firm and solid, which difficulty has here¬ 
tofore interfered with the complete success of the larger 
flexible pipes, is here overcome by separating the bell into 
two parts, so as to permit both the front and rear parts of 
the packing to be driven. 

In putting together this joint, the loose ring is passed 
over the ball-spigot and slipped some distance toward the 


Fig. 98. 



centre of the pipe; the ball-socket is then entered into the 
solid part of the bell and its lead joint packing poured and 
snugly driven ; the loose ring is then bolted in position, and 
its lead joint packing is poured and firmly driven, also. 
This secures a solid packing at both front and rear of the 










































WEIGHTS OF CAST-IRON PIPES. 465 

joint, capable of withstanding the strain that comes upon it 
as the pipe is lowered into position, and ensures a tight 
joint. The ball-spigot is turned smooth in a lathe to true 
spherical form. 

Fig. 98 illustrates J. B. Ward’s patent flexible joint. 

400. Thickness Formulas Compared. —The results 
given by some of the well-known formulas for thicknesses 
of cast-iron pipes, may be compared in Table No. 97. 

401. Formulas for Weights of Cast-iron Pipes.— 
The mean weight of cast-iron is about 450 pounds per cubic 
foot, or .2604 pounds per cubic inch. 

Let d be the diameter of a cast-iron pipe, in inches; 
t , the thickness of the pipe-shell, in inches ; and n the ratio 
of circumference to diameter (= 3.1416); then the cubical 
volume , in inches, of a pipe-shell (neglecting the weight 
of hub), is, for each foot in length, 

V l = (d + t) x t x tt x 12. (14) 

When the length of a pipe is mentioned, it is commonly 
the length between the bottom of the hub and the end of 
the spigot that is referred to ; that is, the net length of the 
pipe laid, or which it will lay. 

The average weight of a pipe per foot includes the 
weight of the hub, which, as thus spoken of, is assumed to 
be distributed along the pipe. 

The weights of the hubs, of general form shown in 
Fig. 96, and whose dimensions are given in Table No. 95 
(p. 461), increase the average weight per foot of the twelve- 
foot light pipes, approximately, eight per cent.; of the 
medium pipes, seven and one-half per cent.; and of heavier 
pipes, seven per cent. 

The equation for cubical volume of pipe-metal, includ¬ 
ing hub, is 

30 


466 


MAINS AND DISTRIBUTION-PIPES. 


TABLE No. 97. 

Formulas for Thickness of Cast-iron Pipes Compared. 

Assumed static pressure, 75 lbs. per square inch. Assumed tenacity of metal, 18,000 lbs. per 

square inch. 


Authority. 


Equation (12), § 452. 

M. Dupuit. 

J. F. D’Aubuisson.. 

Julius Weisbach_ 

Dionysius Lardner. 

Thomas Box. 

G. L. Molesworth.. 

Wm. J. M. Rankine 

John Neville ... . 
Thos. Hawksley . 
Baldwin Latham . 
James B. Francis. 
Thos. J. Whitman 

M. C. Meigs. 

J. H. Shedd . 

J. F. Ward. 

Jos. P. Davis. 


Equations. 


, (z* + ioo) d ( d \ 

t= ^ ■■■■ + .333 (.--j. 

t = (.coi 6 nd) + .013^ + .32.. 

t = (.015^) + .395. 

t = (.002387200 4 - .34. 

t = (.007 nr) + .38. 

{ Vd ) hd 

t = 1 —- + -15 r + ... 

( 10 ) 25000 

{ .37 for 4" to 12" ) 
.50 “ 12 u 30 > 
.62 “ 30 « 50 ) 

“Vi . 

t — [.0016 (n + 10) d] + .32. 

t = .18 Vd . 

. whd 

‘ = ii.is * ' 25 . 

t = (.000058 hd) + .0152 d + .312. 

t = (.0045 nd) + .4 — .ooii*f. 

t — (.0260416 d) + .25. 

t — (.00008 hd) + .oid + .36. 

t — (.0002 hd) + .30. 

t = (.00475 nd) + .35. 


Diameters. 


4 in. 

12 in. 

24 in. 

48 in. 

Thick¬ 

ness. 

Thick¬ 

ness. 

Thick¬ 

ness. 

Thick¬ 

ness. 

Inches. 

.4172 

Inches. 

•5850 

Inches. 

.8367 

Inches. 

1.3400 

•4055 

.5766 

•8333 

1.3466 

•4550 

•5750 

• 755 ° 

1.115° 

•3899 

.4897 

•6394 

•9389 

•4534 

.6002 

.8204 

1.2608 

•3776 

•5794 

.8069 

1.1750 

.4074 

.6121 

.7242 

1.0684 

.2887 

.5000 

.7071 

1.0000 

•4175 

.6126 

•9053 

1.4902 

.3600 

.6235 

.8818 

1.2470 

•3334 

.5002 

•7504 

1.2508 

.4129 

.6148 

.9176 

1.5232 

.4900 

.6699 

•9397 

1-4795 

•3542 

•5625 

.8750 

1.5000 

•4554 

.6461 

.9322 

1.5000 

•4384 

•7152 

1.1304 

1.9608 

.4496 

.6488 

.9476 

1-5452 


In which t = thickness of pipe wall, in inches. 

d = interior diameter of pipe, in inches. 
h — head of water, in feet 
w = weight of a cubic foot of water, = 62.5 lbs. 
n = number of atmospheres of pressure, at 33 feet each. 
p = pressure of water, in pounds per square inch. 

.S = ultimate tenacity of cast-iron, in pounds per square inch. 













































WEIGHTS OF CAST-IRON PIPES. 


467 


V = (d + t) x'108/xttx 12. (15) 

Let w x be the weight per cubic inch of the metal 
(=.2604 lbs.), and w the average weight per foot of the pipe, 
then we have for equation of average weight per foot, of 
twelve-foot pipes, 

10 — 12 (d -f t) X 1.08£ X rrWi. (16) 

To compute the average weight per lineal foot of an 
18-incli diameter pipe, twelve feet long, and | J inch thick in 

the shell, assign the numerical value to the symbols, and 
the equation is: 

to = 12(18 + .65625) x (1.08 x .65625) x 8.1416 x .2604 
= 129.80 pounds. 

In the equation, 12, tt, and ic x are constants, and may be 
united, and their product (= 9.81687) supply their place in 
the equation, when the equation for average loeiglit per 
foot is, 

to = 9.82 (d + t) x 1.0 8t. (17) 

and for the total weight of a 12-foot pipe : 

W = 117.84 (d +t) x 1.08t. (18) 

462. Table of Weights of Cast-iron Pipes.— The 

following table gives minimum weights of three classes of 
cast-iron pipes, of good, tough, and elastic cast-iron (with 
S = 18,000 lbs.), for heads up to 300 ft.; also, approximate 
weights of lead required per joint for the respective diam¬ 
eters, from 4 to 48 inches, inclusive. 


468 


MAINS AND DISTRIBUTION-PIPES. 


TABLE No. 9 8. 


Minimum Weights of Cast-iron Pipes. 


X , 

a 

H 

W 

S 

« 

Q 

CLASS A. 

Head, 116 feet. 
Pressure, 5c lbs. 

CLASS B. 

Head, 230 feet. 
Pressure, 100 lbs. 

CLASS C. 

Head, 300 feet. 
Pressure, 130 lbs. 

Depth of lead in socket. 

Weights of lead per joint. 

Thickness.* 

1 “8 

M 

A * 

4 >v 2 + 

V S X 

bfir' x 
2-oo 

U Os 

< i 

Total weight of a 
12-foot pipe. 

Thickness. 

u ^ 

8, 

- 2 

bDO * 

+ 
a v* 

0 onS 

p ^ CO 
<L> 6^ 

$ N 

< § 

Total weight of a 
12-foot pipe. 

Thickness. 

1) 

P- 0 

-*-» M 

x 

rj 

tea £ 

c« °o 

Jr; o\ 

Z 11 

< g 

Total weight of a 

12-foot pipe. 

in. j 

in . 

lbs. 

lbs. 

in . 

lbs. 

lbs. 

in. 

lbs. 

lbs. 

in. 

lbs. 

4 ! 

•4333 

18.85 

226.20 

•4311 

20.16 

241.92 

•4477 

20.92 

250.06 


4-25 

6 i 

•4383 

30.07 

360.84 

.4800 

32-83 

393-96 

• 5050 

34-52 

414.19 

1 % 

6.25 

8 

•4734 

42.41 

508.92 

.5289 

47-57 

570.84 

.5622 

50.58 

606.95 


8.25 

IO 

.5083 

56.64 

679.68 

•5777 

64.50 

774.00 

•6x94 

69.11 

829.37 

1% 

10.25 

12 i 

•5433 

72.30 

867.60 

.6266 

83.50 

IOD 2 .OO 

.6766 

90. 12 

1081.46 

2 

13.00 


•5783 

89.40 

1072.80 

•6755 

104.62 

I2 55-44 

.7338 

113.60 

1363.22 

2 

15.00 

16 

.6166 

108.65 

1303.80 

.7277 

128.46 

154152 

•7944 

140.18 

1682 . 16 

2% 

24-25 

18 | 

.6483 

128.20 

1 538 .40 

•7733 

I 53- J 9 

1838.28 

.8483 

168.00 

2016.00 

2 x/ e 

27.25 

20 ! 

•6833 

149.81 

1797.72 

.8222 

180.71 

2168.42 

• 9 3 55 

198.14 

2377.68 

2% 

3°-75 

22 

•7183 

172.97 

2075.64 

.8711 

210.21 

2522.52 

.9628 

232.25 

2787.02 

214 

35-25 

24 

•7533 

197-65 

2371.80 

.9200 

242.OI 

2904. I2j 

1.0200 

268.15 

3217.84 

214 

38-25 

27 

.8058 

2 37-55 

2850.60 

•9933 

2 96 - 3 i 

35 r 9-72 

1.1058 

326.56 

39x8.77 

2% 

51-25 

30 

•8583 

280.75 

3367.80 

1.0666 

349.61 

4195.32 

1.1916 

390.53 

4686.41 

2% 

56.25 

33 

.9108 

3 ° 7-53 

3690.36 

1.1400 

410.67 

4928.04 

x.2775 

460.11 

5521.26 

2% 

62.25 

36 

•9633 

373-88 

4486.56 

1.2183 

478.42 

5741-04 

1 • 3633 

535-19 

6422.28 

2k 

79-50 

40 

1-0333 

449.44 

5393-28 

x- 3 111 

571-74 

6860.88 

1.4778 

043 ■96 

7727.47 

2 V2 

88.75 

44 

1•1033 

527-48 

6329.76 

1.4088 

675-29 

8103.48 

1 • 59 21 

762.69 

9152.26 

2% 

107-75 

48 

1 -1733 

611.81 

7321.18 

1.5066 

787.08 

9444.96 

1.7066 

891.30 

10695.62 

2% 

III.OO 


The following table gives the weights of pipes that have 
been used by various water departments for their maximum 
pressures: 


* Vide thicknesses of pipes in Table No. 93, p. 455. 


















































INTERCHANGEABLE JOINTS. 


469 


TABLE No. 98 a. 

Weights of Cast-iron Pipes, as used in Several Cities for 

their Maximum Pressures. 


t n 
W 
X 
u 
z 


« 

w 

H 

w 

< 


3 

4 
6 
8 

io 

12 

14 

l 6 

20 

24 

3° 

3 6 


X 

0 . 

J 

W 

Q 

< 

-J 


* 

OS 

o 

IS 

w 

£ 


z 

o 

H 

tn 

O 


o 

3 

H 

j 

< 

a 


z 

>• 

* 

O 

O 

Bd 

a 


X 

O 

a 

h 

a 


o 

o 

< 

u 

X 

U 


a 

u 

z 

w 

Q 

> 

o 

Od 

a 


J 

w 

£ 

o 

a 


Cd 

H 

> 

(5 

J 

□ 

< 

a 


c 

Q 

« 

o 

H 


Od 

H 

H 

c/j 

w 

x 

u 

o 

a 


< 

& 

< 

H 

H 

o 


Q 

Z 

o 

3 

1 

u 

a 


a 

w 

x 

x 

< 

•s 

J 


Maximum Head, in feet. 


R. 

R. 

R. 

R. 

I 

s.-p.: 

1 

R. 

R. 

S.-P. 

C p R. & T-J p 
D.-P.| D - F ' 

R. 

R. & 

S. -P. 

0 

00 

H 

218 

198 

170 

125 I 

180 

200 

260 

175 ! 200 I 250 

237 

200 


Average Weights, per lineal foot, in pounds. 


15 

19 

31 

42 

53 

7i 

24 

3 6 

T 3? 

20 

32 

46 

12 

185 

28.' 

4° 

56 

85 




18 

39l 

55 

90 

35 

*8s’ 

24? 

365 

50 

"s 3 i 

86 

81 

105 

.... 

124 

130 



125 

151 

170 

174 

200 

208 

183 


307 

235 

231 




250 

33° 

340 

337 

350 

4072 

325 


422 

405 

458 

.... 

400 

438 

450 

585 

696 

606 

.... 

692 

.... 



332 

49 

64 J 

85 

103 

128 

1785 

239 

338 

472 


34 

49 

85' 


129 ^ 

182 

241 s 

350 

412 


24 

43 

69 

87 

123 


*972 

239 

257 


232 

34 

48 

V 


134 

194 

265 

358 


20 
32 
45 
53 s 
75 


IT 3 

165 

265 

334 


i 14 

'•25 


46 


86 

"125 


14 

20 

3° 

45 

60 

100 


202 

257 


130 

170 

230 

'330 


35 

50 

V 


1292 

i 94 

266 ! 

35 i 


CO 

a 

x 

u 

z 


Cd 

w 

H 

S 

3 

< 


3 

4 
6 
8 

10 

12 

14 

16 

20 

24 

30 

36 

48 


The initials in the horizontal column of heads indicate the systems of pressure, viz., R., res¬ 
ervoir ; S.-P., stand-pipe ; and D.-P., direct pressure. 


4G3. Interchangeable Joints. —•When several classes 
of pipes, varying in weight for similar diameters, enter into 
the same system of distribution, as, for instance, in an un¬ 
dulating town, with considerable differences in levels, there 
is an advantage in making the exterior diameters the con¬ 
stants, instead of the interiors, for then the spigots and bells 
of both plain and special castings, and of valves and 
hydrants, have uniformity, and are interchangeable, as occa¬ 
sion requires, and the different classes join each other with¬ 
out special fittings. 


* The Ottawa pipe weights classed as of 4 and 14 inch diameters are in 
fact 5 and 15 inch diameters respectively. 















































































470 


MAINS AND DISTRIBUTION-PIPES. 


If it is objectionable to increase and decrease the interior 
diameters of the light and heavy classes, then the object 
may be attained by increasing the thickness of the ends of 
the light and medium classes, so far as they enter the hubs. 

4G4. Characteristics of Pipe-Metals,—The metal 
of pipes should be tough and elastic, and have great 
tenacity. In proportion as these qualities are lacking, bulk 
of metal, increased in a geometrical ratio, must be sub¬ 
stituted to produce their equivalents. In our formula given 
above (§ 452) for thickness of cast-iron, it will be re¬ 
membered that we were obliged to add a term of thickness 



j- to enable the pipes to be safely handled. 


If the metal is given great degrees of toughness and elas¬ 
ticity, we may omit, for the larger pipes, this last member 
of the formula ; but now we add to each twelve-foot piece 
of pipe, of 20-inch diameter, five or six hundred pounds; 
36-inch diameter, six or eight hundred pounds, etc., that 
would not be required with a superior metal. 


It is expensive to freight this extra metal a hundred or 
more miles, and then to haul it to the trenches and swing it 
into place, and at the same time to submit to the breakage 
of from three to five per cent, of the castings because of the 
brittleness of the inferior metal. 

It is well known that the same qualities of iron stone, and 
of fuel, may produce from the same furnace very different 
qualities of pigs, and it is the smelter’s business to know, 
and he generally does know, whether he has so proportioned 
his materials and controlled his blast, as to produce pigs 
that when remelted will flow freely into the mould, take 
sharply its form, and become tough and elastic castings. 
The founders will supply a refined and homogeneous iron, 
if such quality is clearly specified, and it is well worthy of 



CHARACTERISTICS OF PIPE METALS. 471 

consideration in the majority of cases whether such iron 
will not be in fact the most economical, at its fair additional 
cost, if extra weight, extra freight and haulage, and extra 
breakage, are duly considered. 

Expert inspectors cannot with confidence pronounce 
upon the quality of the cast metal from an examination 
of its exterior appearance, nor infallibly from the appear¬ 
ance of its fracture. Wilkie says* of the fracture of good 
No. 1 cast-iron, that it shows a dark gray color with high 
metallic lustre ; the crystals are large, many of them shining 
like particles of freshly-cut lead; and that however thin 
the metal may be cast, it retains its dark gray color. It 
contains from three to five per cent, of carbon. This is 
the most fusible pig iron and most fluid when melted, and 
superior castings may be produced from it. 

No. 3 has smaller and closer crystals, which diminish in 
size and brightness from the centre of the casting toward 
the edge. Its color is a lighter gray than No. 1, with less 
lustre. No. 2 is intermediate in appearance and quality 
between Nos. 1 and 3. 

The “bright” “mottled” and “white” irons have still 
lighter colored fractures, with a white “list” at the edges, 
are less fusible, and are more crude, hard, and brittle. 

The mottled and white irons are sometimes produced by 
the furnace working badly, or result from using a minimum 
of fuel with the ore and flux. 

The crystals of the coarser kinds of cast-irons were found 
by Dr. Schott, in his microscopical examinations of frac¬ 
tures, to be nearly cubical, and to become flatter as the 
proportion of carbon decreased and the grain became more 
uniform. 


* ‘‘The manufacture of Iron in Great Britain.” London, 1857. 




472 


MAINS AND DISTRIBUTION PIPES. 


In wrought iron, the double pyramidal form of the cast 
crystal is almost lost, and has become flattened down to 
parallel leaves, forming what is termed the flbre of the iron. 

In steel the crystals have become quite parallel and 
fibrous. 

465. Tests of Pipe Metals.—The toughness and elas¬ 
ticity of pipe metal may be tested by taking sample rings 
of, say, 24-inch diameter, 1-inch width, and f-incli thickness, 
hanging them upon a blunt knife-edge, and then suspending 
weights from them, at a point opposite to their support, 
noting their deflections down to the breaking point; also, by 
letting similar rings fall from known heights upon solid an¬ 
vils. The iron may also be submitted to what is termed the 
“ beam test,” generally adopted to measure the transverse 
strength and elasticity of castings for building purposes. 

In such case the standard bar, Fig. 99, is 3 ft. 6 in. long, 

2 in. deep, and 1 in. broad, and 
is placed on bearings 3 ft. apart, 
and is loaded in the middle till 
broken. 

Iron that has been first skill¬ 
fully made into pigs, from good 
ore and with good fuel, and has 
then been remelted, should sustain in the above described 
beam test, from 4,000 to 4,500 pounds, and submit to a de¬ 
flection of from ^ to J-inch. 

The tenacity of the iron is usually measured by submit¬ 
ting it to direct tensile strain in a testing machine, fitted for 
the purpose. Its tenacity should reach an ultimate limit 
of 25,000 pounds per square inch of breaking section, while 
still remaining tough and elastic. Hard and brittle irons 
may show a much greater tenacity, though making less 
valuable pipes. 


Fig. 99 . 



























































THE PRESERVATION OF PIPE SURFACES. 


473 


4GG. Tlic Preservation of Pipe Surfaces.— The 

uncoated iron mains lirst laid down in London, by the New 
River Company, were supposed to impart a chalybeate 
quality to the water, and a wash of lime-water was applied 
to the interiors of the pipes before laying to remedy this evil. 

Before iron pipes had been long in use, in the early part 
of the present century, in those European towns and cities 
supplied with soft water, it was discovered that tuberculous 
accretions had formed so freely upon their interiors as to 
seriously diminish the volume of flow through the pipes of 
three, four, and six-inch diameters. 

This difficulty, which was so serious as to necessitate the 
laying of larger distribution pipes than would otherwise 
have been necessary, engaged the attention of British and 
continental engineers and chemists from time to time. Many 
experimental coatings were applied, of silicates and oxides, 
and the pipes were subjected to baths of hot oil under 
pressure, with the hope of fully remedying the difficulty. 
A committee of the British Association also inquired into 
the matter in connection with the subject of the preservation 
of iron ships, and instituted valuable experiments, wdiich 
are described in two reports of Robert Mallet to the Asso¬ 
ciation. 

A similar difficulty was experienced with the uncoated 
Ron pipes first laid in Philadelphia and New York. 

In the report of the city engineer of Boston, January, 
1852, mention is made of some pipes taken up at the South 
Boston drawbridge, which had been exposed to the flow 
of Cochituate water nine years. 

He remarks that u some of the pipes were covered inter¬ 
nally with tubercles which measured about two inches in 
area on their surfaces, by about three-quarters of an inch 
in height, while others had scarcely a lump raised in them. 


474 


MAINS AND DISTRIBUTION-PIPES. 


Those which were covered with the tubercles were corroded 
to a depth of about one-sixteenth of an inch; the iron to 
that depth cutting with the knife very much like plumbago.” 
Mr. Slade, the engineer, expressed the opinion, after com¬ 
paring the condition of these pipes with that of pipes exam¬ 
ined in 1852, that the corrosion is very energetic at first, 
but that it gradually decreases in energy year by year. 

The process used by Mons. Le Beuffe, civil engineer of 
"Vesoul, France, for the defence of pipes, as communicated* 
by him to Mr. Kirkwood, chief engineer of the Brooklyn 
Water-works, “consists of a mixture of linseed oil and 
beeswax, applied at a high temperature, the pipe being 
heated and dipped into the hot mixture. 

The varnish of M. Crouziere, tested on iron immersed in 
sea-water at Toulon, by the French navy, consisted of a 
mixture of sulphur, rosin, tar, gutta-percha, minum, blanch 
de ceruse, and turpentine. This protected a jilate of 
wuought iron perfectly during the year it was immersed. 

A process that has proved very successful for the preser¬ 
vation of iron pipes used to convey a.cidulated waters from 
German mines, is as follows :f “The pipes to be coated 
are first exposed for three hours in a bath of diluted sul¬ 
phuric or hydrochloric acid, and afterward brushed with 
water ; they then receive an under-coating composed of 
34 parts of silica, 15 of borax, and 2 of soda, and are ex¬ 
posed for ten minutes in a retort to a dull red heat. After 
that the upper coating, consisting of a mixture of 34 parts 
of feldspar, 19 of silica, 24 of borax, 16 of oxide of tin, 4 of 
fluorspar, 9 of soda, and 3 of saltpetre, is laid over the inte¬ 
rior surface, and the pipes are exposed to a white heat for 
twenty minutes in a retort, when the enamel perfectly unites 


* Vide Descriptive Memoir of the Brooklyn Water-works, p. 43. N. 1867. 
f Vide “ Engineering.” London, Jan., 1872, p. 45. 



PRESERVATION OF PIPE SURFACES 

» 


475 


with the cast-iron. Before the pipes are quite cooled down, 
their outside is painted with coal-tar. The above ingre¬ 
dients of the upper coating are melted to a mass in a cru¬ 
cible, and afterwards with little water ground to a fine 
paste.” 

Prof. Barff, M.A., proposes to preserve iron (including 
iron water-pipes) by converting its surfaces into the mag¬ 
netic or black oxide of iron, which undergoes no change 
whatever in the presence of moisture and atmospheric 
oxygen. 

He says, “ The method which long experience has taught 
us is the best for carrying out this process for the protection 
of iron articles, of common use, is to raise the temperature 
of those articles, in a suitable chamber, say to 500° F., and 
then pass steam from a suitable generator into this cham¬ 
ber, keeping these articles for five, six, or seven hours, as 
the case may be, at that temperature in an atmosphere of 
superheated steam. 

“ At a temperature of 1200° F., and under an exposure 
to superheated steam for six or seven hours, the iron surface 
becomes so changed that it will stand the action of water 
for any length of time, even if that water be impregnated 
with the acid fumes of the laboratory.” 

The first coated pipes used in the United States, w T ere 
imported from a Glasgow foundry in 1858. These were 
coated by Dr. Angus Smith’s patent process, which had 
been introduced in England about eight years earlier. 
Dr. Smith’s Coal Pitch Varnish is distilled from coal-tar 
until the naphtha is entirely removed and the material 
deodorized, and Dr. Smith recommends the addition of five 
or six per cent, of linseed oil. 

The pitch is carefully heated in a tank that is suitable 
to receive the pipes to be coated, to a temperature of about 


476 MAINS AND DISTRIBUTION-PIPES. 

300 degrees, when the pipes are immersed in it and allowed 
to remain until they attain a'temperature of 300° Fall. 

A more satisfactory treatment is to heat the pipes in a 
retort or oven to a temperature of about 310 Fall., and 
then immerse them in the hath of pitch, which is maintained 
at a temperature of not less than 210°. 

When linseed oil is mixed with the pitch, it has a ten¬ 
dency at high temperature to separate and float upon the 
pitch. An oil derived by distillation from coal-tar is more 
frequently substituted for the linseed oil, in practice. 

The pipes should be free from rust and strictly clean 
when they are immersed in the pitch-bath. 

4G7. Varnishes for Pipes and Iron-work.— A good 
tar varnish , for covering the exteriors of pipes where they 
are exposed, as in pump and gate houses, and for exposed 
iron work generally, is mentioned* by Ewing Matlieson, 
and is composed as follows : 30 gallons of coal-tar fresh, 
with all its naphtha retained ; 6 lbs. tallow; 1 \ lbs. resin ; 
3 lbs. lampblack; 30 lbs. fresh slacked lime, finely sifted. 
These ingredients are to be intimately mixed and applied 
hot. This varnish may be covered with the ordinary lin¬ 
seed-oil paints as occasion requires. 

% 

A blade varnish , that has been recommended for out¬ 
door iron work, is comioosed as follows: 20 lbs. tar-oil; 
5 lbs. asphaltum ; 5 lbs. powdered rosin. These are to be 
mixed hot in an iron kettle, with care to prevent ignition. 
The varnish may be applied cold. 

408. Hydraulic Proof of Pipes. —When the cast- 
iron pipes have received their preservative coating, they 
should be placed in an hydraulic proving-press, and tested 
by water pressure, to 300 lbs. per sq. in. ; and while under 


“Works in Iron,” p. 281. London, 1873. 



HYDRAULIC PROOF OF PIPES. 


477 


tlie pressure be smartly rung with a hammer, to test them 
for minor defects in casting, and for undue internal strains. 

Fig. 100 is one of tne most simple forms of hydraulic 
proving-presses. The cast-iron head upon the left is fixed 
stationary, while toward the right is a strong head that is 
movable, and that advances and retreats by the action tf 

Fig. 100. 



the screw working in the nut of the fixed head at the right. 
When the pipe is rolled into position for a test, suitable 
gaskets are placed upon its ends, or against the two heads, 
and then by a few turns of the hand-wheel of the screw, the 
movable head is set up so as to press the pipe between the 
two heads. Levers are then applied to the screw, and the 
pressure increased till there will be no leakage of water at 
the ends past the gaskets. The air-cock at the right is then 
opened to permit escape of the air, and the water-valve at 
the left opened to fill the pipe with water. The hydraulic 
pump and the water-pressure gauge, which are attached at 
the left, are not shown in the engraving. When the pipe is 
filled with water, and the valves closed, the requisite pres¬ 
sure is then applied by means of the pump. Care must be 
taken that all the air is expelled, before pressure is applied, 
lest in case of a split, the compressed air may scatter the 
pieces of iron with disastrous results. 



























































Fig. 101. 



Fig. 102. 



Fig. 100. 




















































CEMENT-LINED AND COATED PIPES. 


479 


469. Special Pipes.—Fig. 101 is a section through a 
single Branch, with side views of lugs for securing a cap or 
hydrant branch. 

Fig. 102 is a section through a Reducer. 

Fig. 103 is a section through a Bend. 


Fig. 104. 


Fig. 105. 



Fig. 104 is a section through a Sleeve, the upper half 
being the form for covering cut ends of j)ipes, and the lower 
half the form for uncut spigot ends. 

Fig. 105 is a part section and plan of a clamp Sleeve. 


WROUGHT-IRON PIPES 

470. Cement-Lined and Coated Pipes.—Sheet-iron 
water-pipes, lined and coated with hydraulic cement mor¬ 
tar, by a process invented by Jonathan Ball, were laid in 
Saratoga, N. Y., to conduct a supply of water for domestic 
purposes to some of the citizens, as early as 1845. 

The inventor, who was aware of the ready corrosion of 
wrought-iron when exposed to a flow of water and to the 
dampness and acids of the earth, had observed the pre¬ 
servative influence of lime and cement when applied to iron, 
and saw that with its aid, the high tensile strength of 









































480 


MAINS AND DISTRIBUTION-PIPES. 


wrought or rolled iron, could be utilized in water-pipes to 
sustain considerable pressures of water, and the weight of 
the iron inquired, thus be materially reduced. 

The reduction in the weight of the iron reduced also the 
total cost of the complete pipe in the trench. 

The favorable qualities of hydraulic cement as a conduc¬ 
tor of potable waters had long been well-known, for the 
Romans invariably lined their aqueducts and conduits 
with it. 

Twenty-five or thirty towns and villages, and a number 
of corporate water companies had already adopted the 
wrouglit-iron cement-lined water pipes in their systems, and 
still others were experimenting with it at the breaking out 
of the civil war in 1861. 

As one result of the war, the price of iron * rose to more 
than double its former value, and the difference in cost be¬ 
tween cast and wrought iron pipes became conspicuous, and 
the cost of all pipes rose to so great total sums that the pipe 
of least first cost must of necessity be adopted in most 
instances, almost regardless of comparative merits. So 
long as the high prices of iron and of labor remained firm, 
the contractors for the wrouglit-iron were enabled to lay it 
at a reduction of forty per cent, from the cost of the cast- 
iron pipe. 

Increased attention to sanitary improvements led many 
towns to complete their water supplies even at the high 
rates, and many hundred miles of the cement-lined pipes 
came into use. 

471. Methods of Lining.—Its manufacture is simple. 
The sheet-iron is formed and closely riveted into cylinders 

* New York and Philadelphia prices current record the nearly regular 
average monthly increase in the price of Anthracite Pig Iron No. 1, from 18f 
dollars per ton of 2240 pounds in August, 1861, to 73f dollars per ton in 
August, 1864. 




COVERING. 


481 


of seven or eiglit feet in length, and of diameter from one 
to one and one-half inches greater than the clear bore of the 
lining is to be finished. The pipe is then set npright and a 
short cylinder, of diameter equal to the desired bore of the 
pipe, is lowered to the bottom of the pipe. Some freshly 
mixed hydraulic cement mortar is then thrown into the pipe 
and the cylinder, which has a cone-shaped front; and guid¬ 
ing spurs to maintain its central position in the shell, is 
drawn up through the mortar. A uniform lining of the 
mortar is thus compressed within the wrought-iron shell. 
The ends are then dressed up with mortar by the aid of a 
small trowel or spatula, and the pipes carefully placed upon 
skids to remain until the cement is set. 

The interiors of the pipe-linings are treated to a wash of 
liquid cement while they are still fresh, so as to fill their pores. 

In another process of lining, a smoothly-turned cylin¬ 
drical mandril of iron, equal in length to the full length of 
the pipe, and in diameter to the diameter of the finished 
bore, is used to form the bore, and to compress the lining 
within the shell. A fortnight or three weeks is required for 
the cement to set so as safely to bear transportation or haul¬ 
age to the trenches. In the meantime the iron is or should 
be protected from storms and moisture, and also from the 
direct rays of the sun, which unduly expands the iron, and 
separates it from a portion of the cement lining. 

47£. Covering.—When these pipes are laid in the 
trench, a bed of cement mortar is prepared to receive them, 
and they are entirely coated with about one inch thickness 
of cement mortar, as is shown in the vertical section of a 
six-inch pipe, Fig. 106. 

The writer has used upwards of one hundred miles of 
this kind of pipes, and the smaller sizes have proved uni¬ 
formly successful. 

31 


482 


MAINS AND DISTRIBUTION-PIPES. 


Fig. 106. 



The iron is relied upon wholly to sustain the pressure 
of the water and resist the effects of water-rams. The 
cement is depended upon to preserve the iron, which object 
it has accomplished during the term these pipes have been 
in use, when the cement was good and workmanship faith¬ 
ful, which, unfortunately for this class of pipe, has not 
always been the case, and the reputation of the pipe has 
suffered in consequence. 


Fig. 107. 



473. Cement-Joint.—A sheet -iron sleeve, about eight 
inches long, as shown in Fig. 107, is used in the common 
form of joint to cover the abutting ends of the pipe as they 
are laid in the trench. 

The diameter of the sleeve is about one inch greater than 
the diameter of the wrouglit-iron pipe shell, and the annular 
space between the pipe and sleeve is filled with cement. The 
sleeve and pipe are then covered with cement mortar. 

In a more recently patented form of pipe, the shell has a 
taper of about one inch in a seven-foot piece of pipe, and 

























CAST HUB-JOINTS. 


483 


the small end of one piece of pipe enters about four inches 
into the large end of the adjoining pipe, thus forming a 
lap without a special sleeve. The thickness of lining in 
these pipes varies, but the bore is made uniform. 

d74:. Cast Hub-Joints. —The writer having experienced 
some difficulty with both the above forms of cement-joints, of 
the larger diameters, and desiring to substitute lead pack¬ 
ings for the cement, in a 20-inch force main, to be subjected 
to great strains, devised the form of joint shown in Fig. 108. 


Fig. 108. 



In this case the wrought-iron shells were riveted up as 
for the common 20-inch pipe, and then the pipe was set 
upon end in a foundry near at hand, a form of bell moulded 
about one end, and molten iron poured in, completing the 
bell in the usual form of cast-iron bell. A spigot is cast 
upon the opposite end in a similar manner. The lead pack¬ 
ing is then poured and driven up with a set, as the pipes 
are laid, as is usual with cast-iron pipes. The joint is as 
successful in every respect as are the lead-joints of cast-iron 
pipes. 

The force-main in question has been in use upwards of 
three years, and water was, during several months of its 

































484 


MAINS AND DISTRIBUTION-PIPES. 


earliest use, pumped through, it into the distribution pipes, 
on the direct pumping system. 

For lead joints on wrought-iron pipes from ten to sixteen 
inches diameter inclusive, about four inches width of the 
edge of the spigot end sheet may be rolled thicker, so as to 
bear the strain of caulking the lead, as a substitute for the 
cast spigot. 

475. Composite Branches. — The wrought - iron 
branches were originally joined to their mains by the appli¬ 
cation of solder, the iron being tirst tinned near and at the 
junction. After the successful pouring of the bells, the 
experiment was tried of uniting the parts by pouring molten 
metal into a mould, formed about them, the metal being 

Fig. 109. 



cast partly outside and partly inside the pipes, as in the 
case of the hub-joint. The parts were rigidly and very sub¬ 
stantially united by the process, which is in practical effect 
equal to a weld. 

Fig. 109 shows a section of a double six-inch branch on 
a twelve-inch sub-main. 


















































THICKNESS OF SHELLS FOR CEMENT LININGS. 485 

Fig. 110 is a section of a wrought-iron angle with, its 
parts united by a cast union. 

Several holes, similar to the rivet holes of the pipe, are 
punched near the ends to be united at different points in 
the circumference, so that the metal flows through them, 
as shown in the sketches. 


Fig. 110. 



The writer has used these branches and angles exclu¬ 
sively in several cities, in wrought-iron portions of the 
distribution-pipes, without a single failure. 

47G. Thickness of Shells for Cement Linings.— 
When computing the thickness of sheets for the shells of 
wrought-iron cement-lined pipes, the internal diameter of 
the shell itself, and not of finished bore, is to be taken. 
The longitudinal joints of the shells for pipes of 12-inch and 
greater diameters, should be closely double riveted. 

The tensile strength of the shells, when made of the best 
plates, may be assumed, if single riveted, 36,000 pounds 
per square inch, and double riveted 40,000 pounds per 
square inch. 

A formula of thickness, given above, with factor of 
safety = 4, in addition to allowance for water-ram, may be 
used to compute the thickness of plates, viz.: 

^ _ (p + 100 )d 


( 19 ) 















486 


MAINS AND DISTRIBUTION-PIPES. 


in which t is the thickness of rolled plate, in inches. 
d “ diameter of the shell, in inches. 

<p “ static pressure due to the head in lbs. per 
sq. in. = .434^. 

S “ tenacity of riveted shells, in lbs. per. sq. in. 

The following table gives the thickness of shells for 
cement linings, and the nearest No. of Birmingham gauge 
in excess, suitable for heads of -from 100 to 300 feet, by 
formula, 

+ 100 )d 

Z - ^T>=v • 


TABLE No. 9 9. 

Thickness of Wrought Iron Pipe Shells. 

(Diameters 4" to 10" single riveted, 5 = 36,ooolbs. Diameters 12" and upward, double riveted, 

.S' = 40,000 lbs.) 




Head ii6 Feet. 

Head 175 Feet. 

Head 300 Feet. 

Diameter 
of Bore. 

Diameter 
of Shell. 

Thickness 

by 

Formula. 

Nearest 
No. Birm. 
Gauge in 
Excess. 

Thickness 

by 

Formula. 

N earest 
No. Birm. 
Gauge in 
Excess. 

Thickness 

by 

Formula. 

Nearest 
No. Birm. 
Gauge in 
Excess. 

Inches. 

4 

Inches. 

5 

Inches. 

.0417 

x 9 

Inches. 

.0486 

l8 

Inches. 

.0639 

l6 

6 

7 

.0528 

17 

.0681 

x 5 

.0894 

13 

8 

9 * 2 5 

.0771 

15 

.0899 

1 3 

. 1182 

11 

IO 

11.25 

•°937 

13 

. IO94 

12 

• I 437 

9 

12 

T 3- 2 5 

.0994 

12 

• 1T 59 

11 

• x 5 2 4 

8 

14 

1 5* 2 5 

• 1144 

12 

•1334 

IO 

• 1 754 

7 

16 

17-5 

•1313 

IO 

•I 53 2 

8 

. 2012 

6 

i8 

* 9-5 

.1463 

9 

. 1706 

7 

.2242 

5 

20 

21.5 

.1613 

8 

.1881 

6 

. 2472 

3 

22 

2 3-5 

•1763 

7 

. 2056 

5 

.2702 

2 

24 

2 5-5 

• l 9 l 3 

6 

.2236 

4 

.2932 

1 


Shells having less factors of safety than our formula 
gives, have been used in many small works. A factor 
equal to 6, to include effect of water-ram, should always be 



























LINING COVERING, AND JOINT MORTAR, 


487 


taken, and this may be found directly by a formula in the 
following form: 

f = ;33M§' ( 20) 

477. Gauge Thickness and Weights of Rolled 

Iron.—The following table (No. 100) gives the thicknesses 
and weights of sheet-iron, corresponding to Birmingham 
gauge numbers; also thicknesses and weights increasing 
by sixteenths of an inch. 

478. Lining, Covering, and Joint Mortar.—The 

lining mortar and covering mortar should have the volume 
of cement somewhat in excess of the volume of voids in the 
sand, or, for linings, equal parts of the best hydraulic 
cement and line-grained, sharp, silicious sand; and, for 
coverings, two-lifths like cement and three-fifths like sand. 

The joint mortar should be of clear cement, or may be 
of four parts of good Portland cement, and one part of 
hydraulic lime, with just enough water to reduce it to a 
stiff paste. 

This kind of pipe demands very good materials for all 
its parts, and the most thorough and faithful workmanship. 

A concrete foundation should be laid for it in quicksand, 
or on a soft bottom, and a bed of gravel, well rammed, 
should be laid for it in rock trench, and exceeding care 
must be taken in replacing the trench back-fillings. Poor 
materials or slighted workmanship will surely lead to after 
annoyance. 

Some of the cement-lined pipes are given a bath in hot 
asphaltum before their linings are applied. In such case, a 
sprinkling of clean, sharp sand over their surfaces imme¬ 
diately after the bath, while the coating is tacky, assists in 
forming bond between the cement and asphaltum. 



488 


MAINS AND DISTRIBUTION-PIPES. 


TABLE No. 1 OO. 

Thicknesses and Weights of Plate-iron. 


Birming¬ 

ham 

gauge 

Thickness. 

Weight of a 
square foot. 

Thickness, 

in 

sixteenths 

Thickness, 
in decimals of 
an inch. 

Weight of 
a square foot. 

No. 



of an inch. 



Inches. 

Pounds. 

Inches. 

Inches. 

Pounds. 

QOOO 

•454 

i8 -35 

I 

J 2 

.03125 

I.263 

OOO 

•425 

17.18 

I 

T(T 

.06250 

2.526 

OO 

.38 

15-36 

3 

3 2 

.09375 

3.789 

O 

•34 

: 3-74 

I 

"S' 

.12500 

5 *° 5 2 

I 

•3 

12.13 

5 

~ 5~2 

A 5625 

6.315 

2 

.284 

I I.48 

3 

in 

.1875° 

7-578- 

3 

• 2 59 

IO -47 

7 

T2 

.21 §75 

8.841 

4 

.238 

9.619 

I 

.25000 

IO.IO 

5 

.22 

8.892 

9 

TT 

.28125 

ii -37 

6 

.203 

8.205 

5 

TF 

• 3 1 250 

12.63 

7 

.18 

7.275 

I I 

'3 2 

•34375 

13.89 

8 

.165 

6.669 

3 

. 375 oo 

15.16 

9 

.148 

5.981 

13 

3 2 

40625 

16.42 

IO 

• 134 

5.416 

7 

TIT 

.43750 

17.68 

11 

.12 

4.850 

I 5 

.46875 

18 -95 

12 

. 109 

4 - 4 o 5 

1 

2 

.50000 

20.21 

13 

•°95 

3.840 

9 

T6" 

•56250 

22.73 

14 

.083 

3-355 

5 

■S’ 

.62500 

25.26 

15 

.072 

2.910 

I I 

Y6~ 

.68750 

27.79 

16 

.065 

2.627 

3 

Y 

.75000 

30 . 3 1 

17 

.058 

2-344 

I 3 

TF 

.81250 

32.84 

18 

.049 

1.980 

7 

■S’ 

.87500 

35-37 

19 

.042 

1.697 

I 5 

T^T 

.93750 

37-89 

20 

•°35 

1-415 

I 

1 

40.42 

21 

.032 

x - 293 


1.06250 

42.94 

22 

.028 

1.132 


1.12500 

45-47 

2 3 

.025 

1.010 


1.18750 

48.00 

2 4 

.022 

.8892 


1.25000 

5 °- 5 2 

2 5 

.02 

.8083 

: tV 

1.31250 

53-05 

26 

.018 

.7225 


1.37500 

55-57 

2 7 

.016 

.6467 

i tV 

1.43750 

58.10 

28 

.014 

•5658 

ij 

1.50000 

60.63 

2 9 

.013 

•5254 

T 9 

1.56250 

63 . T 5 

30 

.012 

.485° 


1.62500 

65.68 

3 i 

.010 

.4042 

I fJ 

1.68750 

68.20 

3 2 

.009 

• 3 6 3 8 

if 

1.75000 

70.73 

33 

.008 

•3233 

i tJ 

1.81250 

73.26 

34 

.007 

.2829 

if 

1.87500 

75-78 

35 

.005 

.2021 

T 15 

1 176 

i. 9375 o 

78.31 

3 6 

.004 

. 1617 

2 

2 

80.83 




























ASPHALTUM-BATH FOR PIPES. 


489 


479. Asphaltum-coated Wrought-iron Pipes.— 

Wrought-iron pipes, coated with asplialtum, have been 
used almost exclusively in California, Nevada, and Oregon, 
some of those of the San Francisco water supply being 
thirty inches in diameter. 

Some of these wrought-iron pipes, in siphons, are sub¬ 
jected to great pressure, as, for instance, in the Virginia 
City, Nevada, supply main, leading water from Marlette 
Lake. 

This main is 11J inches diameter, and 87,100 feet in 
length, and crosses a deep valley between the lake, upon 
one mountain and Virginia City upon another. The inlet, 
where the pipe receives the water of the lake, is 2,098 feet 
above the lowest depression of the pipe in the valley, where 
it passes under the Virginia and Truckee Railroad, and the 
delivery end is 1528 feet above the same depression. A 
portion of the pipe is subjected to a steady static strain of 
750 pounds per square inch. 

The thickness of this pipe-shell varies, according to the 
pressure upon it, as follows : 


Head, in feet.•< 

200 

200 

330 

430 

57 ° 

700 

950 

1050 

1250 

1400 

or 

to 

to 

to 

to 

to 

to 

to 

to 

and 

l 

less. 

33 ° 

430 

57 ° 

700 

95 ° 

1050 

1250 

1400 

over. 

No. of iron, Birmingham gauge... 

16 

15 

14 

12 

II 

9 

7 

5 

3 

0 

Thickness, in inches. 

.065 

.O72 

.083 

.IO9 

.12 

00 

M 

.18 

.22 

•259 





The joints are covered with a sleeve, and the joint pack¬ 
ing is of lead. 

480. Asplialtum-Batli for Pipes. —A description of 
the asphaltum coating, as prepared for these pipes by 
Herman Schussler, C.E., under whose direction many pipes 
have been laid, is given in the January, 1874, Report of 
J. Nelson Tubbs, Esq., Chief Engineer of the Rochester 
Water-works, as follows, in Mr. Schussler’s language : 
















490 


MAINS AND DISTRIBUTION-PIPES. 


“ The purest quality of asphaltum (we use the Santa 
Barbara) is selected and broken into pieces of from the size 
of a hen’s egg to that of a fist. With this, three or four 
round kettles are tilled full, then the interstices are tilled 
with the best quality of coal tar (free from oily substances), 
and boiled from three to four hours, until the entire kettle 
charge is one semi-tiuid mass, it being frequently stirred up. 
The best and most practical test then, as to the suitability 
of the mixture, is to take a piece of sheet iron of the thick¬ 
ness the pipe is made of, say six inches square, it being 
cold and freed from impurities, and dip it into the boiling 
mass, and keep it there from five to seven minutes. Imme¬ 
diately after taking it out, plunge it into cold water, if 
possible near the freezing-point, and if, after removal from 
the water, the coating don’t become brittle, so as to jump 
off the iron in chips, by knocking it with a hammer, but 
firmly adheres (like the tin coating to galvanized iron), the 
coat is good and will last for ages. If, on the other hand, 
it is brittle, it shows that there is either too much oil in the 
tar or asphaltum, or the mixture was boiled too hot, or 
there was too much coal-tar in the mixture ; as adding coal- 
tar makes the mixture brittle, while by adding asphaltum 
it becomes tough and pliable. The pipes are immersed in 
the bath as thus prepared.” 

Wrouglit-iron pipes of this description are extensively 
used in France, in diameters up to 48 inches. 

They are first subjected to a bath of hot asphaltum, and 
then the exteriors are coated with an asphaltum concrete, 
into which some sand is introduced, as into the cement¬ 
covering above described. 

481. Wrought Pipe Plates.— The shells of wrouglit- 
iron conduits and pipes should be of the best rolled plates, 
of tough and ductile quality, of ultimate strength not less 


WYCKOFF’S PATENT PIPE. 


491 


than 55,000 lbs. per square inch, and that will elongate 
fifteen per cent, and reduce in sectional area twenty-five per 
cent, before fracture. 

WOOD PIPES. 

482. Bored Pipes.— The wooden pipes used to replace 
the leaden pipes, in London, that were destroyed by the 
great fire, three-quarters of a century ago, reached a total 
length exceeding four hundred miles. These pipes were 
bored with a peculiar core-auger, that cut them out in 
nests, so that small pipes were made from cores of larger 
pipes. 

The earliest water-mains laid in America were chiefly of 
bored logs, and recent excavations in the older towns and 
cities have often uncovered the old cedar, pitch-pine, or 
chestnut pipe-logs that had many years before been laid by 
a single, or a few associated citizens, for a neighborhood 
supply of water. 

Bored pine logs, with conical faucet and spigot ends, 
and with faucet ends strengthened by wrought-iron bands, 
were laid in Philadelphia as early as 1797. 

Detroit had at one time one hundred and thirty miles of 
small wood water-pipes in her streets. 

483. Wyckoflf’s Patent Pipe. —A patent wood pipe, 
manufactured at Bay City, Michigan, has recently been 
laid in several western towns and cities, and has developed 
an unusual strength for wood pipes. Its chief peculiarities 
are, a spiral banding of hoop-iron, to increase its resistance 
to pressure and water-ram; a coating of asplialtum, to 
preserve the exterior of the shell; and a special form of 
thimble-joint. 

Fig. Ill is a longitudinal section through a joint of this 
wood pipe, showing the manner of inserting the thimble, 


492 


MAINS AND DISTRIBUTION-PIPES, 


Fig. 111. 



and Fig. 112 is an exterior view of the pipe, showing the 
spiral handing of lioop-iron, and the asphaltum covering. 

The manufacturer’s circular, from which the illustra¬ 
tions are copied, states that the pipes made under this 


Fig. 112. 



patent are from white pine logs, in sections eight feet long. 
The size of the pipes is limited only by the size of the suit¬ 
able logs procurable for their manufacture. 

Judged by schedules of factory prices, these pipes do 
not appear to be cheaper in first cost than wrought-iron 
pipes. 






















































Figs. 114, 115. 



coffin’s stop—valve. (Boston Machine Co., Boston.) 


















































































































































































































CHAPTEE XXII. 

DISTRIBUTION SYSTEMS, AND APPENDAGES. 

484. Loss of Head by Friction. —In the chapter 
upon flow of water in pipes (XIII, ante\ we have discussed 
at length the question of the maximum discharging ca¬ 
pacities of pipes. When planning a system of distribution 
pipes for a domestic and fire service, it is quite as import¬ 
ant to know how much of the available head will be con¬ 
sumed by, or will remain after, the passage of a given 
quantity of water through a given pipe. 

For a really valuable fire service, the effective head 
pressure remaining upon the pipes, with fult draught , 
should be, in commercial and manufacturing sections of a 
town, not less than one hundred and fifty feet , and in 
suburban sections, not less than one hundred feet. 

Water at such elevations, near a town, has a large com¬ 
mercial value, whether it has been lifted by the operations 
of nature and retained by ingenuity of man, or has been 
pumped up through costly engines and with great expend¬ 
iture of fuel. 

When such head pressures are secured at the expense 
of pumps and fuel, they are too costly to be squandered in 
friction in the pipes. Such frictional loss entails a corre¬ 
sponding daily expense of fuel so long as the works exist. 
In such case, the pipes may be economically increased in 
size until the daily frictional expense capitalized, approxi¬ 
mates to the additional capital required to increase the 
given pipes to the next larger diameters. 


494 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


The frictional head h" in pipes under pressure, is found 
by the formula, 

h" = e 2 (4m) (1) 

The frictional head for a given diameter is as the square 
of the velocity, nearly ( v 2 m) and, for different diameters, 
inversely as the diameters. 

The coefficient* m decreases in value as the velocity 
increases, and for a given velocity decreases as the diameter 
increases. 

485. Table of Frictional Heads in Pipes.—The 

following table (No. 101, p. 495) we have prepared to facili¬ 
tate frictional head calculations, and to show at a glance the 
frictional effect of increase of velocity, in given pipes from 
4 to 36 inch diameters. The second and last columns show 
also the theoretical volume of delivery through clean, smooth 
pipes at different given velocities, f 

The fourth column gives approximate values of the 

i 

coefficient m for given diameters and velocities, and for 
clean smooth pipes under pressure. 


* Vide Table No. 62, page 248, of coefficients (m) for clean, slightly tuber- 
culated, and foul pipes ; also § 274, page 250, for formula of frictional resist¬ 
ance to flow. 

f There will be a slight reduction of volume and velocity, and increase of 
coefficient and friction, for each valve and branch, and material changes in 
these respects if the pipes are rough or foul. 




FRICTIONAL HEADS IN PIPES. 


495 


\ 


TAB LE No. 101. 

Frictional Head in Main and Distribution Pipes (in each 
1000 feet length). Ji — v* 


Diara. 

of 

pipe. 

Volume of 
water 
delivered 

Velocity 

of 

flow. 

Coefficient 

of 

friction. 

Frictional head 
per 1000 feet. 

U. S. gallons 
in 24 hours. 

Inches. 

Cu. ft. per 
7 nin. 

Feet per 
second. 


Feet. 

Gallons. 

4 

5 

•958 

.00714 

1.221 

53.856 


7-5 

1-437 

.00695 

2.675 

80,784 


IO 

1.916 

.00680 

J^. 653 

107,712 


12.5 

2.387 

.00666 

7.114 

134,640 


15 

2.865 

.00654 

10.96 

161,568 


17-5 

3-342 

.00644 

13.03 

188,496 


20 

3-83* 

.00633 

17.32 

215,424 

6 

17-5 

1.409 

.00666 

1.643 

188,496 


20 

1.701 

.00655 

2.355 

215,424 


22.5 

I-9I3 

.00648 

2.946 

242,352 


25 

2.126 

.00646 

3.628 

269,280 


27-5 

2-339 

.00638 

4.337 

296,208 


30 

2.551 

.00634 

5.126 

323-136 


35 

2.976 

.00623 

6.855 

376,992 


40 

3.401 

.00615 

8.838 

430,848 


45 

3.827 

.00610 

11.100 

484,704 

8 

30 

1.429 

.00644 

1.225 

323A36 


35 

1.685 

.00635 

1.680 

376,992 


40 

1.910 

.00628 

2.124 

430,848 


45 

2.143 

.00620 

2.654 

484,704 


50 

2.381 

.00615 

3.249 

538,560 


55 

2.619 

.00609 

3.893 

592,416 


60 

2.857 

.00603 

4.587 

646,272 


65 

3-095 

.00600 

5.356 

700,128 


70 

3-331 

.00596 

6.159 

753,984 


75 

3-571 

.00592 

7.035 

807,840 


80 

3.820 

.00589 

7.963 

861,696 


85 

4.048 

.00586 

8.948 

9 1 5,552 


90 

4.298 

.00584 

10.056 

969,408 

10 

60 

1.835 

.00614 

1.541 

646,272 


70 

2.141 

.00606 

2.071 

753,984 


80 

2.447 

.00597 

2.665 

861,696 


9° 

2.752 

.00590 

3.331 

969,408 


100 

3.058 

.00584 

4.071 

1,077,120 


no 

3-364 

.00578 

4-876 

1,184,832 


120 

3.670 

.00572 

5.743 

1,292,544 


130 

3-976 

.00569 

6.706 

1,400,256 


140 

4.281 

.00566 

7.733 

1,507,968 


150 

4.587 

.00562 

8.815 

1,615,680 


* Take d in feet. Vide p. 504. 





















496 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


TABLE No. 101—(Continued). 


Frictional Head in Main and Distribution Pipes (in each 

1000 feet length). 


Diam. 

of 

pipe. 

Volume of 
water 
delivered. 

Velocity 

of 

flow. 

Inches. 

Cu. ft. per 

Feet per 


min . 

Second. 

12 

120 

2.548 


140 

2.972 


l6o 

3-397 


180 

3.821 


200 

4.246 


220 

4.668 


24O 

5.098 

14 

175 

2.721 


200 

3.109 


225 

3-498 


250 

3.887 


275 

4-275 


300 

4.665 


325 

5-053 


350 

5-457 

i6 

225 

2.682 


250 

3-099 


275 

3.281 


300 

3 - 57 f> 


325 

3-874 


350 

4.172 


375 

4.471 


400 

4.768 


425 

5.066 


450 

5-368 


475 

5.666 


500 

5.961 

18 

300 

2.830 


350 

3-301 


400 

3-773 


450 

4-245 


500 

4-717 


550 

5.188 


600 

5.660 


650 

6.132 


675 

6.367 


Coefficient 

of 

friction. 

Frictional head 
per 1000 feet. 

U. S. gallons 
in 24 hours. 


Feet. 

Gallons. 

.00581 

2.31$ 

1,292,544 

.00571 

3.133 

1,507,968 

.00563 

4.036 

1,723,392 

.00555 

5.033 

1,938,816 

.00551 

6.171 

2,154,240 

.00546 

7.407 

2,369,664 

.00542 

8.755 

2,585,088 

.00560 

2.207 

1,884,960 

.00553 

2.845 

2,154,240 

.00546 

3.550 

2,423,520 

.00542 

4.359 

2,692,800 

•00537 

4.989 

2,962,080 

.00538 

6.232 

3,231,360 

.00530 

7.203 

3,500,640 

.00524 

8.738 

3,769,920 

.00554 

1.857 

2,423,520 

.00538 

2.408 

2,692,800 

.00536 

2.599 

2,962,080 

.00530 

3.158 

3,231,360 

.00526 

3.679 

3,500,640 

.00523 

4.21$ 

3,769,920 

.00520 

4.844 

4,039,200 

.00518 

5.488 

4,308,480 

.00515 

6.159 

4 , 577,760 

.00508 

6.81$ 

4,847,040 

.00510 

7.657 

5,116,320 

.00507 

8.395 

5,385,600 

.00530 

1.758 

3,231,260 

.00519 

2.31$ 

3,769,920 

•00513 

3.024 

4,308,480 

.00508 

3.791 

4,847,040 

.00504 

4.644 

5,385,600 

.00499 

5.562 

5,924,160 

.00497 

6.594 

6,462,720 

.00495 

7.708 

7,001,280 

.00494 

8.293 

7,270,560 






















FRICTIONAL HEADS IN PIPES, 


497 


TABLE 10 1—(Continued). 

Frictional Head in Main and Distribution Pipes (in each 

iooo feet length). 


Diam. 

of 

pipe. 

• 

Volume of 
water 
delivered. 

Velocity 

of 

flow. 

Coefficient 

of 

friction. 

F rictional head 
per 1000 feet. 

U. S. gallons 
in 24 hours. 

Inches. 

Cu. ft. per 
min. 

Feet per 
second. 


Feet. 

Gallons. 

20 

350 

2.674 

.00516 

1.375 

3.769,920 


400 

3-056 

.00509 

1.731 

4,308,480 


450 

3-433 

.00503 

2.215 

4,847,040 


500 

3.821 

.00500 

2.720 

5,385,600 


550 

4.202 

.00496 

3.264 

5,924,160 


600 

4-585 

.00493 

3.862 

6,462,720 


650 

4.967 

.00490 

4.505 

7,001,280 


700 

5-341 

.00487 

5.177 

7,539,840 


750 

5-731 

.00484 

5.924 

8,078,400 


800 

6.113 

.00481 

6.698 

8,616,960 


850 

6.495 

.00479 

7.710 

g.^s.sso 


900 

6.878 

.00477 

8.409 

9,694,080 

24 

550 

2.918 

.00484 

1.280 

5,924,160 

600 

3-183 

.00482 

1.517 

6,462,720 


650 

3-449 

.00477 

1.762 

7,001,280 


700 

3-714 

.00475 

2.035 

7,539.840 


750 

3-979 

.00473 

2.326 

8,078,400 


800 

4-245 

.00471 

2.636 

8,616,960 


850 

4.510 

.00469 

2.963 

9 A 55.520 


900 

4-775 

.00467 

3.307 

9,694,080 


950 

5.041 

.00466 

3.678 

10,232,640 


1000 

5 - 3 o 6 

.00464 

4.057 

10,771,200 


1050 

5-571 

.00463 

4. 463 

11,309,760 


1100 

5-835 

.00462 

4.871 

11,848,320 


1150 

6.100 

.00459 

5.684 

12,386,880 


1200 

9-367 

.00457 

5.754 

12,925,440 


1250 

6.633 

.00455 

6.218 

13,464,000 

27 

800 

3-353 

.00465 

1.410 

8,616,960 

900 

• 

3-772 

.00461 

1.811 

9,694,080 


1000 

4.192 

.00457 

2.217 

10,771,200 


1100 

4.611 

.00453 

2.659 

11,848,320 


1200 

5-030 

.00451 

3.150 

12,925,440 


1300 

5-454 

.00449 

3.687 

14,002,560 


1400 

5.868 

.00447 

4.250 

15,079,680 


1500 

6.287 

.00445 

4.856 

16,156,800 


1600 

6.707 

.00443 

5.502 

17,233,920 


1700 

7.126 

.00439 

6.155 

18,311,040 


32 




















498 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


TABLE No. lOl—(Continued). 

Frictional Head in Main and Distribution Pipes (in each 

1000 feet length). 


Diam. 

of 

pipe. 

Volume of 
water 
delivered. 

Velocity 

of 

flow. 

Coefficient 

of 

friction. 

Frictional head 
per 1000 feet. 

U. S. gallons 
in 24 hours. 

Inches. 

Cu. ft. per 
77 iin. 

Feet per 
second. 


Feet. 

Gallons. • 

30 

1000 

3-396 

.00448 

1.284 

10,771,200 


1200 

4-075 

.00441 

1.820 

12,925,440 


1400 

4-754 

.00438 

2.4.GO 

15,079,680 


1600 

5-433 

.00434 

3.257 

17 , 233,920 


1800 

6.112 

.00429 

4.009 

19,388,160 


2000 

6.791 

.00428 

4 *904 

21,542,400 


2200 

7.471 

.00425 

5.894 , 

23,696,640 


2400 

8.149 

.00421 

6.947 

25,850,880 

36 

1500 

3-536 

.00419 

1.085 

16,156,800 


2000 

4.708 

.00412 

1.891 

21,542,400 


2500 

5-894 

.00406 

2.920 

26,928,000 


3000 

7-073 

.00401 

4.154 

32,313,600 


3500 

8.252 

.00397 

5.598 

37,699,200 


4000 

9-431 

.00394 

7.257 

43,084,800 


486. Relative Discharging Capacities of Pipes.— 

The volume of water delivered, q , by a pipe, is, as we have 
seen (§ 296), equal to the product of its section S, into its 
mean velocity of flow v, 

q = JSv. 

The equation of velocity is, 


v = 


%gri \|. 
m f 9 


hence we have, for full pipes, 

fjrrin = s . | Mi !* = , 7854(Z2 . ( 2jM 

( m ) I 4 m ) ( 4m ) 

By uniting the two terms of d , within the vinculum, we 

( lid 5 ) i 

have the equation of volume, q = 6.302 j J- , and 























RELATIVE CAPACITIES OF PIPES. 


499 


= Vg. j • 61685^') i 


4 m 


V2(/h • 


.6168 5d 5 ) * 

4mZ ) ^ 


For a given inclination, all the terms in the right-hand 
member are constant, except d and m. We have then the 

/ /75 

relative discharging powers of pipes, as the quotients, \/ —, 

V Tfb 

or nearly as the square roots of the fifth powers of the 
diameters. 

By transposition of the equation for volume, q , we have 


the equation for diameter of long pipes, d — .4789 


5 /4 mlq 1 


h 


and 


r , | 1 ^ 4 (fm [ i _ j 1 4 mZ ^ 2 

- I 2^ X J31685* f “ I 2g7i X ^1685 


( 3 ) 


By this we perceive that the relative diameters required 
for equally effective deliveries are as the products q l m , or 
nearly as the fifth roots of the squares of the volumes. 

487. Table of Relative Capacities of Pipes.— The 
following table (No. 102) of approximate relative discharg¬ 
ing powers of pipes, will facilitate the proper proportioning 
of systems of pipe distributions. It shows at a glance the 
ratio of the square root of the fifth power of any diameter, 
from 3 to 48 inches, to the square root of the fifth power of 
any other diameter within the same limit. 

In the second column of this table, the diameter 1 foot 
is assumed as unit, and the ratios of the square roots of the 
fifth powers of the other diameters, in feet , are given oppo¬ 
site to the respective diameters in feet written in the first 
column. Thus the approximate relative ratio of discharging 
power of a 3-foot pipe to that of a 1-foot pipe is as 15.588 to 
1 ; and of a .5 foot pipe to a 1-foot pipe as .1768 to 1; also 
the relative discharging power of a 4-foot pipe (— 48-inch) 
is to that of a 2-foot pipe (= 24-incli) as 32 to 5.657 ; and of 











500 


DISTRIBUTION 


SYSTEMS, AND APPENDAGES. 


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DEPTHS OF PIPES. 


501 


a 2.5-foot pipe to the combined discharging powers of a 
2-foot and 1.5-foot pipes as 9.859 to (5.657 + 2.756). 

The last vertical column gives the diameters in inches, 
as does also the horizontal column at the head of the right- 
hand section of the table. 

The numbers in the intersections of the horizontal and 
vertical columns from the diameters in inches give also 
approximate relative discharging capacities. For instance, 
it* we select in the vertical column of diameters that of the 
48-inch pipe and desire to know how many smaller pipes it 
is equal to in discharging capacity, we trace along the hori¬ 
zontal column from it, and find thgt it is equal to 15.59, 
sixteen-inch pipes, or 5.65 t wenty-four-incli pipes, or 1.58 
forty-inch pipes, etc. Also, for other diameters, we find 
that a 24-inch pipe is equal to 32 six-inch pipes, or 2.05 
eighteen-inch pipes, and a 12-incli pipe is equal to 5.65 six- 
inch pipes. 

488. Depths of Pii)es. —The depths at which pipes 
are to be placed, so they shall not be injured by traffic or 
frost, is a matter for special local study, general rules being 
but partially applicable. The depth is controlled in each 
given latitude, or thermic belt, by first, the stability of the 
earth, whether it be soft and quaky, or heavy clay, or close 
sand, or rock ; second, whether the ground be saturated by 
surface waters that remain and freeze and conduct down 
frost, or by living springs flowing up and opposing deep 
penetration of frost; third, whether the ground be porous, 
well underdrained to a level below the pipes, and the pores 
filled with air, which is a good non-conductor ; and fourth, 
whether the winds sweep the snows off from given localities 
and leave them unprotected, or given localities are shaded 
and the severity of night is uncounteracted at noonday. 

Along those thermic lines whose latitudes at the Atlan- 


502 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


tic coast are as given, the depths of-the axes of the pipes, in 
close gravelly soils, may be approximately as follows: 


TABLE No. 103. 

Approximate Depths for Axes of Water-pipes. 


Diam. 

Latitude 
40° North. 

Latitude 
42 0 North. 

Latitude 
44° North. 

Diam. 

Latitude 
40° North. 

Latitude 
42° North. 

Latitude 
44° North. 


Depth of 

Depth of 

Depth of 


Depth 0/ 

Depth 0/ 

Depth 0/ 


axis. 

axis. 

axis. 


axis. 

axis. 

axis. 

u 

/ // 

/ n 

/ // 

// 

/ n 

t n 

f u 

4 

4-8 

5—2 

6—2 

20 

4 —10 

5 — 5 

6—3 

6 

4-8 

5—2 

6—2 

22 

4—10 

5 — 5 

6—3 

8 

4—7 

5 —i 

6—2 

24 

4—11 

5- 6 

6—4 

IO 

4—7 

5 —i 

6—2 

27 

4—11 

5 — 7 

6-4 

12 

4-7 

5 —i 

6—2 

30 

5— 0 

5- 8 

6—4 

14 

4—7 

5—2 

6—2 

33 

5— 0 

5 — 9 

6—5 

16 

4-8 

5—3 

6—2 

36 

5— 0 

5—10 

6—6 

18 

4—9 

5—4 

6—3 

40 

5 — 1 

5 —11 

6—7 


There is a general impression that the water passed into 
pipes, will in a very short time take the temperature of the 
ground in which the pipes are laid. Close observation does 
not confirm this impression. 

If water at a high temperature is admitted to a deep 
pipe system, in the early summer, while the ground is yet 
cool, the consumers will derive but little benefit from the 
coolness of the earth, and this is especially the case when 
the pipes are coated and lined with cement. 

Frost also penetrates at various points as low as the 
bottoms of sub-mains, without seriously interfering with 
the flow, and water-pipes are often suspended beneath 
bridges, where ice forms in the river near by, a foot or more 
in thickness, without their flow being interfered with. An 
eight or ten inch pipe will resist cold a long time before it 
will freeze solid. 

The hydrants, small dead ends, and service-pipes are 
























RATES OF CONSUMPTION OF WATER. 


503 


most sensitive to cold, and tlieir depths and coverings should 
receive especial attention. 

Dead ends should he avoided as much as possible, and 
circulation maintained for the protection of the pipes against 
frost, as well as to maintain the purity, or to prevent the 
fermentation of the motionless water. 

489. Elementary Dimensions of Pipes. —A table 
of the elementary dimensions of pipes facilitates so much, 
j)ipe calculations, that we insert it here (p. 504). The last 
column gives also the quantity of water required to fill each 
lineal foot of the pipes, when laid complete, or the quan¬ 
tities they contain. 

490. Distribution Systems. —We have now reduced 
to tabular form the data that will assist in establishing the 
proportions of the several parts of a system of distribution 
pipes, for the domestic and fire supply of a town or city. 

For illustration, let us assume a case of a thriving young 
city of 25,000 inhabitants, situated on the bank of a naviga¬ 
ble river, and that the contour of the land had permitted 
its streets to be straight, and to intersect at right-angles. 
In such case its system of distribution pipes will form a 
series of parallelograms, inclosing one, two or more of the 
city blocks, as circumstances require, substantially as is 
shown in the plan of a system of pipes, Fig. 113. 

491. Rates of Consumption of Water. —The healthy 
growtli of the city gives reason to anticipate an increase to 
35,000 inhabitants within a decade, and this number at 
least should be provided for in the first supply main, the 
first reservoir, and such parts as are expensive to duplicate, 
and a larger number should be provided for in the con¬ 
duit, and such parts as are very expensive and difficult to 
duplicate. 

The continued popularization of the use of water, and 


504 


DISTRIBUTION SYSTEMS, AND APPENDAGES, 


TAB LE N o. 1 04. 

Elementary Dimensions of Pipes. 


Diameter 

Diameter. 

Contour. 

Sectional area. 

Hydraulic 
mean radius. 

Cubical con¬ 
tents per lineal 
foot. 

Inches. 

Feet. 

Feet. 

Sp. feet. 


Cubic feet. 

I 

.0417 

.1310 

.OOI366 

.OI04 

.OOI366 

3 

T 

.0625 

.1965 

.003068 

•OI56 

.003068 

I 

.083 

.2618 

.005454 

.0208 

•005454 


.1250 

• 39 2 7 

.OI227 

.0312 

.OI227 


•H 5 8 

• 45 81 

.01670 

•0364 

.01670 

2 

.1667 

• 5 2 35 

.02185 

.0418 

.02232 

3 

.250 

• 7 8 54 

.04909 

.0625 

.04909 

4 

•3333 

1-047 

.08726 

•0833 

.08726 

6 

.5000 

1 - 57 * 

•19635 

.1250 

• x 9 6 35 

8 

.6667 

2.094 

• 349 ° 

. 1666 

• 349 ° 

IO 

• 8 333 

2.618 

•5454 

. 2083 

•5454 

12 

1.0000 

3 - T 4 2 

• 7 8 54 

. 2500 

•7854 

14 

1.1667 

3-665 

1.069 

.2916 

1.069 

16 

1-3333 

4.189 

1 • 397 

•3333 

1 • 39 7 

18 

1.5000 

4.713 

i - 7 6 7 

• 375 ° 

!• 7 6 7 

20 

1.6667 

5-235 

2.181 

.4166 

2. l8l 

24 

2.0000 

6.283 

3.142 

.5000 

3.142 

27 

2.2500 

7.069 

3-976 

•5625 

3-976 

30 

2.5000 

7- 8 54 

4.909 

.6250 

4.909 

33 

2.750° 

8.639 

5 - 94 o 

.6875 

5-940 

36 

3.0000 

9-425 

7.069 

•75oo 

7.069 

40 

3-3333 

10.47 

8.726 

•8333 

8.726 

44 

3.6667 

it.52 

IO - 5 S 8 

.9166 

10.558 

48 

4.0000 

12.56 

I2.567 

1.0000 

12.567 

54 

4.5000 

14.14 

I 5 - 9°5 

1.1250 

I5-905 

60 

5.0000 

i5-7i 

! 9- 6 35 

1.2500 

1 9-635 

72 

6.0000 

19.29 

29.607 

1.5000 

29.607 

84 

7.0000 

21.99 

38.484 

1.7500 

38.484 

96 

8.0000 

2 5-45 

50.265 

2.0000 

50.265 


























PLAN OF A DISTRIBUTION SYSTEM. 






















































































506 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


the increasing demand for it for domestic, irrigating, orna¬ 
mental, and mechanical purposes, with the increasing waste 
to which they all tend, requires that at least an annual 
average of 75 gallons per capita daily must be provided for 
the 35,000 persons. 

In our discussion of the varying consumption of water 
(§ 10), it is shown that in certain seasons, days of the week, 
and hours of the day, the rate of consumption, independent 
of the fire simply, is seventy-five per cent, greater than the 
average daily rate for the year. In anticipation of this 
varying rate, we should proportion our main for not less 
than fifty per cent, increase (= 75 x 1.50 = 112.5), or for a 
rate of 112.5 gallons per capita daily, which for 35,000 per¬ 
sons equals a rate of 365 cubic feet per minute. 

492. Hates of Fire Supplies.— For fire supply we 
anticipate the possibility of two fires happening at the same 
time requiring ten hose streams each. The minimum fire 
supply estimate is, then, twenty hose streams of say 20 
cubic feet per minute, or a total of 400 cubic feet per minute. 

The combined rate of flow of fire and domestic supply is 
(365 + 400) 765 cubic feet per minute. 

493. Diameter of Supply Main.— Turning now to the 
table of Frictional Head in Distribution Pipes, and looking 
for volume in the second column, we find that a 24-inch 
pipe will deliver 765 cubic feet per minute, with a velocity 
of flow of about 4 feet per second, and with a loss of head 
of about 2.5 feet in each thousand feet length of main. A 
20-inch pipe will deliver the same volume with a velocity 
of flow of about 5.75 feet per second, and with a loss of 
head of about 6 feet in each thousand feet length. Unless 
the main is short, this velocity, and this loss of head, in¬ 
creased by the loss at angles and valves, is too great. We 
adopt, therefore, the 24-inch diameter for supply main. 


MAXIMUM VELOCITIES OF FLOW. 


507 


494. Diameters of Sub-Mains. —We now compute 
the portions of the whole supply that will be required in 
each section of the city. If our plan of distribution is 
divided into twelve sections, then the average section sup¬ 
ply is one-twelfth of the whole. We find, for instance, that 
Sec. 1 requires 85 per cent, of the average ; Sec. 3, 125 per 
cent, of the average ; Sec. 12, 100 per cent, of the average ; 
Sec. 22, 95 per cent, of the average, etc. 

Xow, with the aid of the table of relative discharging 
powers of pipes, and the table of frictional heads in pipes, 
We can readily assign the diameters to the sub-mains that 
are to distribute the waters to the several sections, adding 
to the domestic and fire supply volumes for the nearest 
sections the estimated volumes that are to pass beyond them 
to remoter sections. 

This done, we may sum up the frictional losses of head 
along the several lines from the supply to any given point, 
and deduct the sum from the static head, and see if the 
required effective head remains. The volume and effective 
head are matters of the utmost importance, when the pipes 
are depended upon exclusively to supply the waters re¬ 
quired for fire extinguishment. The lack of these has cost 
several of our large cities a million dollars and more in a 
single night. 

An inspection of the table of Frictional Head shows how 
rapidly the friction increases when velocity increases. The 
increase of frictions are, in the same pipe, as the increase of 
squares of velocities ( v 2 m ), nearly. 

495. Maximum Velocities of Flow. —As a general 
rule, the velocities in given pipes should not exceed, in feet 
per second, the rates stated in the following table for the 
respective diameters. 


508 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


TABLE No. 105. 

Maximum Velocities of Flow in Supply and Distribution Pipes. 


Diameter, in inches. 

4 

6 

8 

IO 

12 

14 

16 

18 

20 

22 

24 

27 

30 

33 

36 

Velocity, in ft. per sec.. 

2-5 

2.8 

3 

3-3 

3-5 

3-9 

4.2 

4-5 

4-7 

5 

5-3 

5-8 

6.2 

6.6 

7 


496. Comparative Frictions. —As regards friction 
alone in any given pipe, it does not matter whether the 
water is flowing np a hill or down a hill, or materially if 
the pressure is great or little; or in long, conical, and 
smooth pipes, whether the water is flowing toward the large 
end or toward the small end. The total friction will he the 
same in both directions in the first case, and will also be the 
same in both directions in the last case. In the conical 
pipe, however, the friction per unit of length, or per lineal 
foot, will be less than the average at the large end, because 
the velocity of flow will be less there, and more than the 
average at the small end. The total frictional head will be 
the same as though the whole pipe had a uniform diameter 
just equal to the diameter in the conical pipe at the point 
where the friction is equal to the average for the whole 
length. 

497. Relative Rates of Flow of Domestic and 
Fire Supplies. —The actual consumption of water by the 
fire department for the extinguishment of fires, in any city, 
per annum, is very insignificant when compared with either 
the domestic, the irrigation and street sprinkling, or the 
mechanical supply for the same limit of time, yet it has 
appeared above that the pipe capacity required for the fire 
service, in the general main of a small city, exceeds that 
required for the whole remaining consumption. If we 
examine this question still closer, taking a length of 1200 
feet of distribution pijDe in a closely built up section of the 



















REQUIRED DIAMETERS FOR FIRE SUPPLIES. 


509 


city, we find on tlie 1200 feet length, say 40 domestic service 
pipes, and consumption of say 750 gallons each per day, or 
total of 15000 gallons per day. Making due allowance for > 
fifty per cent, increase of liow at certain hours, we have a 
required delivery capacity of 1.5 cubic feet per minute to 
cover this whole consumption. On the same 1200 feet of 
pipe there are, say four fire-hydrants. If in case of fire we 
take from these hydrants only four streams in all, of 20 
cubic feet per minute each, we require a delivery capacity 
of 80 cubic feet per minute. In this case, which is not an 
uncommon one, the required capacity for the fire service is 
to that for the remaining service as 80 to 1.5. 

If the given pipe, 1200 feet long, is a six-incli pipe, sup¬ 
plied at both ends, then the delivery for fire at each end is 
forty cubic feet per minute. Referring to the table of fric¬ 
tional head, we find that this quantity requires a velocity of 
fiow of 8.401 feet per second, and consumed head, in fric¬ 
tion, at the rate of 8.8 feet per thousand feet. 

If the 80 cubic feet per minute must all come from one 
end of the pipe, then the pipe should be eight inches diam¬ 
eter, in which case the velocity will be nearly four feet per 
second and the head consumed at the rate of about eight 
feet per thousand feet length. 

498. Required Diameters for Fire Supplies.— 
As a general rule, the minimum diameters of pipes for sup¬ 
plying given numbers of hydrant streams, when the given 
pipes are one thousand feet long, and static head of water 
one hundred and fitly feet, are as follows: 


510 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


TABLE No. 10 6. 

Diameters of Pipes for Given Numbers of Hose Streams. 


Number of hose streams... 

Approximate total quantity of water, 

in cubic feet per minute. 

Required diameter of pipe, in inches.. 

i 

20 

4 

2 

40 

6 

3 

60 

8 

4 

80 

8 

5 

100 

10 

6 

120 

10 

^ OO 

T H 

M 

8 

160 

12 

9 

180 

12 

IO 

200 

12 

11 

220 

12 

12^ 

240 

14 

Number of hose streams. 

13 

14 

15 

l6 

*7 

18 

J 9 

20 

21 

22 

23 

24 

Approximate total quantity of water, 
in cubic feet per minute. 

260 

280 

3 °° 

320 

340 

360 

380 

400 

420 

440 

460 

480 

Required diameter of pipe, in inches.. 

14 

14 

14 

l6 

16 

l6 

l6 

l6 

l6 

18 

18 



If the pipes are short, the velocities of How may he 
increased somewhat, for a greater ratio of loss of head per 
unit of length is then permissible. y 

If the pipe is supplied from both ends, then the number 
of hose streams may be doubled without increase of the 
frictional head ; hence the advantage of so distributing the 
sub-mains as to deliver a double supply to as many points 
as possible, for this is equivalent to doubling the capacity 
of the minor pipes. If the pipes are several thousand feet 
long, and have a large proportionate domestic draught, 
then a due increase should be given to the diameters. 

499. Duplication Arrangement of Sub-Mains.— 
When the sub-mains can be distributed in parallel lines, at 
several squares distance, and “gridironed” across by the 
smaller service mains, as in the plan, Fig. 113, or arranged 
in some equivalent manner, then a most excellent system 
will be secured. In such case, if an accident happens to a 
pipe, or valve, or hydrant, in any central location, there are 
at least two lines of sub-mains around that point, and the 
supply will with certainty be maintained at points beyond. 

Pipes are always liable to accident in consequence of 
building excavations, sewerage excavations, sewer over¬ 
flows, quicksand or clay slides, floods, and various other 
causes that cannot be foreseen when the pipes are laid ; and 


































STOP-VALVE SYSTEM. 


511 


when new hydrants are to be attached, or large pipe con¬ 
nections to be made, or repairs to be made, it is frequently 
necessary to shut off the water. The advantage of dupli¬ 
cate lines of supply to all points is apparent in such case. 
When a city has become dependent on its pipes for its 
water supply and protection from fire, it is absolutely neces¬ 
sary that the supply be maintained, and the result may be 
disastrous if it fails for an hour. 

500. Stop-Valve System.— It is equally advantage¬ 
ous to have a sufficient number of stop-valves, or “gates,” 
as they are frequently 
termed, upon the pipe, 
so the water may be shut 
off from any given point 
without cutting off the 
supply from both a long 
. and a broad territory, or 
even a very long length 
of pipe. The sub-main 
parallelogram system 
shown in the plan, Fig. 

113, permits of such an ar¬ 
rangement of stop-valves, 
chiefly of small diameters 
and inexpensive, that an 
accident at any point will 
not leave that point with¬ 
out a tolerable fire pro¬ 
tection from both sides. 

For instance, if it is 
necessary to shut off in 
section 2 a part of East 
Fourth Street between Avenues A and D, the hydrants at 
































































































































512 DISTRIBUTION SYSTEMS, AND APPENDAGES. 

the corners of East Third and Fifth Streets will still he avail¬ 
able. If the gates are placed at each branch from the sub- 
mains, and at the intersections of the sub-mains, as they 
should be, then an accident to a sub-main will not neces¬ 
sitate the shutting off of any service-main joining it, for the 
service-main supplies can be maintained from the opposite 
ends. Wherever cross service-mains are required, as in 
Avenues B and C, in Section 3 in the plan, they may pass 
under the other service-mains whose lines they cross and 
have gates at their end branches only, which admits of their 
being readily isolated. 

501. Stop-Valve Locations. —A systematic disposi¬ 
tion of the pipes generally should be adopted. If the pipes 
are not placed in the centres of streets, they should be placed 
with strict uniformity at some certain distance from the 
centre of the street, and carefully aligned, and uniformly 
upon the same geographical side, as, upon the northerly and 
westerly side. The stop-valves should be disposed also, 
with rigid system, as, always in the line of the street boun¬ 
dary, the line of the curb, or some fixed distance from the 
centre of the street. An accident may demand the prompt 
shutting of any gate of the whole number, at any moment 
of day or night; and if, perchance, its curb-cover is hidden 
by frozen earth or by snow, it is important to know exactly 
where to strike without first journeying to the office and 
searching for a memorandum of distances and bearings. 
Searching for a gate-cover buried under frozen earth is a 
tedious operation, and it is not always possible to uncover 
every one of several hundred gates after every thaw and 
every snow-storm in winter. 

Strict adherence to a system in locating gates enables 
new assistants to readily learn and to know the exact posi¬ 
tion of them all. 


STOP-VALVE DETAILS. 


513 


Strict adlieience to system in locating pipes is requisite 
for tlie strict location of gates, and pipes should be cut, if 
necessary, to bring tlie gates to their exact locations. If a 
gate is a half-length of pipe out of position, it may cost 
several hours delay in digging earth frozen hard as a sand¬ 
stone rock, to find the gate-cover. 

Blow -oft, and Waste Valves*—"When pipes are 
located upon undulating ground, blow-off valves and pipes 
will be required in the principal depressions of the mains 
and sub-mains, to flush out the sediment that is deposited 
from unfiltered water. The diameters of the blow-off pipes 
may be about half the diameters of the mains from which 
they branch. Smaller wastes will answer for the drainage 
of the service-main sections for repairs or connections, and 
these may lead into sewers, or wherever the waste-water 
may be disposed of. 

503. Stop-Valve Details.—A variety of styles of stop- 
valves are now offered by different manufacturers, and a 
special advantage is claimed for each, so that no little prac¬ 
tical sagacity is required on the part of the engineer to pro¬ 
tect his works from the introduction of weak and defective 
novelties, that may prove very troublesome. 

He must observe that the valve castings are so designed 
as to be strong and rigid in all parts, that there are no thin 
spots from careless centring of cores; that flat parts, if any, 
are thickened up, or ribbed, so they will not spring ; that 
the valve-disks are so supported as not to spring under 
great pressures, and that they and their seats are faced with 
good qualities of bronze composition and smoothly scraped, 
ground, or planed, and that they will not stick in their 
seats ; that the valve-stems are particularly strong and stiff, 

9 

with strong square or half-V threads, and that they and 
their nuts are of a tough bronze or aluminum composition. 

33 


514 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


Fig. 119. 


Fig. 119 a. 




Ludlow’s Stop-valve— (Ludlow Manufacturing Co., Troy). 

Figs. 114 to 119a illustrate the principal features of 
valves that have been well introduced. 

A majority of the good,valves have double disks, that 
are self-adjusting upon their seats, and their seats are 
slightly divergent, so that the pressure of the screw can set 
the valve-disks snug upon the seats. 

The loose disks should have but a slight rocking move¬ 
ment between their guides, and must not be permitted to 
chatter when the valve is partially open. 

The blow-off valves may be solid or single-disk valves, 
but the valves in the distribution must be tight against 
pressure from both and either sides, whether the difference 
of pressure upon the two sides be much or little. 

Yalves exceeding twenty inches diameter are usually 
placed upon their sides, except in chambers, and the disks 
have lateral motions, or sometimes the valve-cases are so 

































































































VALVE CURBS. 


515 


arranged that the disks have vertical downward motions. 
Otherwise the water in the valve-domes would he too much 
exposed to frost in winter, as it would rise nearly to the 
ground surface. 

504. Valve Curbs. —The stop-valve curbs are some¬ 
times of chestnut or pitch-pine plank, with strong cast-iron 
covers, and sometimes of cast-iron, placed upon a founda¬ 
tion of bricks laid in cement. 

The plank curbs are about eighteen by twenty-four 
inches dimensions at top, flaring downward according to 


Fig. 120. 



the size of the valve, and they are often of such dimensions 
as to admit a man, with room to enable him conveniently to 
renew the packing about the valve-stem. 























516 


DISTRIBUTION SYSTEMS, A&D APPENDAGES. 


The cast-iron curbs are usually elliptical in section. 
The writer has used in several cities, for the smaller gates, 
up to twelve inches diameter, circular curbs (Fig. 120) of 
beton coignet , with cast-iron necks and covers. The neck is 
six inches clear diameter at the road surface, fifteen to 
eighteen inches deep, according to the size of the valve, and 
flares to the size of the cement curb, which is just large 
enough to slip over the dome-flange of the valve-case. The 
cement curb rests upon a foundation of brick or stone laid 
in cement mortar. 

When these are paved about, the whole surface exposed 
is only seven and one-half inches diameter, and they are 
not as objectionable in the streets as the larger covers. 

All gate-curbs must be thoroughly drained, so that 
water cannot stand in them, and freeze in winter. 

505. Fire-Hydrants.—The design of a fire-liydrant 
that is a success in every particular is a great achievement. 
It ranks very nearly with the design of a successful water- 
meter. 

Nearly every speculative mechanic, it would seem, who 
has had employ in a machine-shop for a time, has felt it 
his duty to design the much-needed successful hydrant; as 
so many doctors and lawyers have grappled with, and 
believed for a time, that they had solved the great meter 
problem. 

Innumerable patterns of hydrants are urged upon water 
companies and engineers, and are accompanied by an 
abundance of certificates setting forth their excellence ; and 
many of them have good points and will answer all practi¬ 
cal purposes until an emergency comes, when they fail, and 
the experiment winds up with a loss that would have paid 
for a thousand reliable hydrants. 

A considerable practical experience with hydrants, and 


HYDRANT DETAILS. 


517 


Fig. 121 . 


> 


an expert knowledge of the qualities demanded in the 
design and materials of a hydrant, are necessary to enable 
one to judge at sight of the value of a new pattern. 

506. Post-Hydrants. —In the smaller 
towns and in the suburbs of cities, post- 
hydrants , of which Fig. 121 illustrates one 
pattern, are more generally preferred, as 
they are more readily found at night, and 
are usually least expensive in first cost. 

They are placed on the edge of the 
sidewalk, and a branch pipe from the 
service main furnishes them with their 
water. If the service main is of sufficient 
capacity, the post-hydrant may have one, 
two, three, or four nozzles. In cities where 
steam fire-engines are used, a large nozzle 
is added for the steamer supply, and if 
there is a good head pressure, two nozzles 
are usually supplied for attaching leading 
hose. 

For the supply of two hose streams, or 
a steamer throwing two or more streams, 
the hydrant requires a six-inch branch 
pipe from the service main, and a valve of 
equal capacity. The supply to post-hy¬ 
drants has too often been throttled down, 
when there was no head pressure to 
spare, and the effectiveness of the hy¬ 
drant very much reduced thereby. 

507. Hydrant Details.—In New 
England and the Northern States, a 
frost-case is a necessary appendage to 
a post-hydrant, and it must be free to 


PI PE TO MAIN 


Mathew’s Hydrant— 
(R. D. Wood & Co., 
Philadelphia). 































































































(518 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


move up and down with the expansion and contraction of 
the earth, without straining upon the hydrant base. In 
clayey soils, these frost cases are often lifted several inches 
in one winter season, and if the post is not supplied with 
the movable case in such instances, it is liable to be torn 
asunder. 

A waste-valve must be provided in every hydrant that 
will with certainty drain the hydrant of any and all water 
it contains as soon as the valve is closed, and the waste 
must close automatically as soon as the valve begins to 
open. 

The main valve must be positively tight , or great trouble 
will be experienced with the hydrant in severe winters. A 
moderate leakage, as in some stop-valves, cannot be per¬ 
mitted. A free drainage must be provided to pass away 
the waste water from the hydrant, or, if the hydrant is fre¬ 
quently opened, for testing or use, the ground will soon be¬ 
come saturated and the hydrant cannot properly drain. 

If the valve closes “with” the pressure there must be 
no slack motion of its stem, or when the valve is being 
closed and lias nearly reached its seat, the force of the cur¬ 
rent will throw it suddenly to its seat and cause a severe 
water-ram. 

The screw motion of hydrant valves must be such that 
the hydrant cannot be suddenly closed, or with less than 
ten complete revolutions of the screw. The valves should 
move slowly to their seats in all cases, as, if several hydrants 
happen to be closed simultaneously, the water-ram caused 
thereby may exert a great strain upon the valves, and the 
shock will be felt to some extent throughout the whole 
system of pipes. The sudden closing of a hydrant may 
make a gauge, attached to the pipes, that is more than a 
mile distant, kick up fifty or sixty pounds. 


HYDRANT DETAILS. 


519 


Fig. 122 . 


If a hydrant branch is taken from a main-pipe or sub- 
main, there should be a stop-valve between the main and 
hydrant, so the hydrant may be repaired without shutting 
off the flow through the main. 

In 1874 the writer made some 
measurements of the quantities of 
water delivered, under different 
heads, through Boston Machine 
Co. Post Hydrants, which are sim¬ 
ilar in form to the Mathews Hy¬ 
drant (Fig. 121). The volume of 
water was measured by passing it 
through a 3-inch Union water-meter, 
which was connected to each hy¬ 
drant by a length of fire-hose. 

The length of hose between the 
hydrant and meter in each and 
every experiment was 49 feet 10 
inches. The bores of the hydrant 
nozzles and of the hose and meter 
couplings were two and one-quar¬ 
ter inches diameter. The hydrant 
branches were six inches in di¬ 
ameter, and hydrant barrels four 
and one-lialf inches diameter. The 
lengths of hose given, following, 
were in all cases beyond the meter, 
and were attached to the meter. 

The hydrant was filled with 
water and pressure without flow, taken by a gauge just 
previous to the beginning of each test. 

The following tests, at different elevations, covers a range 
of head pressures between 42 feet and 183 feet: 



FLUSH HYDRANT. 



























































52 0 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


TABLE No. 107. 

Experimental Volumes of Hydrant Streams. 


Remarks. 


A. 42 Feet Head- 


Open nozzle of meter, 2 \ inch diameter 
| inch nozzle attached to meter. 


t1 “ 
8 

U 

<< << 

(i 

T1 “ 

€i 

on 55 feet 

^ inch of hose, 

ii “ 

a 

“ 108 “ 

ni “ “ “ , 

Open 

butt of 

108 “ 

ii^ “ “ « , 



B. llO 

Feet Head. 


Open nozzle of meter, 2\ inch diameter .... 

i|- inch nozzle attached to meter... 

i| “ “ on 53 feet ii inches of hose 

ii « “ “ io 8 “ ni “ “ “ 

C. 136 .5 Feet Head. 

Open nozzle of meter, 2\ inch diameter. 

inch nozzle attached to meter. 

ii “ “ on 55 feet ^ inch of hose. 


D. 183.18 Feet Head. 


ii- inch nozzle 

on 55 feet 

10 

inches of hose 

X 1 << K 

± H 

“ 108 lf 


<< U ii 

T 1 u (< 

8 

“ 162 “ 

7 

ii ii ii 

Open butt of 

162 “ 

7 

ii ii ii 


Pressure 
before 
test. lbs. 

Delivery 
cu. ft. 

per minute. 

18.23 

20.376 

a 

9-372 

a 

12.550 

a 

12.096 

a 

11.382 

a 

15-342 

47-74 

40.OOO 

ii 

24.666 

a 

21.276 

a 

20.408 

59-24 

43-974 

ii 

24.390 

a 

23.526 

79-5 

27.648 

a 

25-974 

a 

24.648 

a 

33.672 


Friction of flow in ordinary fire-hose consumes pressure 
rapidly, the reduction being directly in proportion to the 
length, and also as the square of the volume or velocity of 
water flowing, except as the couplings disturb these nearly 
uniform increments. The friction in 2 £ inch ordinary fire¬ 
hose will be found approximately by the following formulas 
expressing loss of head in pounds, p, per square inch. 


For rubber hose, 


Icf 

P ~ 2820 cW ’ 



2520 d s ’ 



for leather hose, 


P = 


( 5 ) 































PRESSURE LOST BY FRICTION IN FIRE HOSE. 520 a 

in which l — length of hose in feet, q = gallons of water 
discharged from the hose per minute, and d the diameter 
of the hose in inches. 

The following table of friction loss in hose has been 
computed from published data of the valuable experiments 
of Messrs. Ellis and Leshure. 


TABLE No. 107«. 

Pounds Pressure lost by Friction in each ioo feet of 2-J 
inch Fire-Hose, for given Discharges of 
Water per Minute. 


Diam. of 

N ozzles. 

Head, in lbs. per sq. in 
“ “ feet .... 

Pressure at Hose Nozzle. 

20 

46.2 

30 

69-3 

40 

92.4 

50 

ii5-5 

60 

138.6 

70 

161.7 

80 

184.8 

90 

207.9 

IOO 

231.0 


( Gallons discharged . 

no 

134 

155 

173 

189 

205 

219 

232 

245 

i in. 

•< Rubber hose, lbs ...... 

4-35 

6.40 

8.40 

10.20 

12.80 

14.80 

17.00 

19.20 

20.50 


( Leather hose, lbs. 

6-33 

8.53 

10.83 

13. 10 

15-34 

I 7-79 

20.11 

22.40 

24.83 


( Gallons discharged . ,. 

139 

I70 

196 

219 

240 

259 

277 

294 

310 

in. 

•< Rubber hose, lbs. ..... . 

6.79 

10.16 

13.60 

17-05 

20.59 

24.00 

27.OO 

30.00 

33-oo 


( Leather hose, lbs . 

9-°5 

I2.7I 

16.38 

20.11 

23.88 

27.61 

3 I -4 I 

35-24 

39-07 


( Gallons discharged. 

171 

210 

242 

271 

297 

320 

342 

363 

383 

114 in. 

-< Rubber hose, lbs. 

10.28 

15.64 

20.85 

25.46 

29.50 

39.00 

43.81 

49.42 

55 -oo 


( Leather hose, lbs. 

12.84 

19.00 

24.07 

30.11 

35-94 

4 I *57 

47-36 

53-25 

59.20 


( Gallons discharged 

20 7 

253 

293 

327 

358 

387 

4i3 

439 

462 

in. 

-< Rubber hose, lbs_... , 

15.00 

22.96 

29.40 

40.50 

48.20 

55-70 

64.70 

72.00 

79.26 


( Leather hose, lbs . ..... 

18.81 

26.39 

35-oi 

43-38 

52.00 

60.40 

68.59 

76-73 

84.87 




































520 b DISTRIBUTION SYSTEMS, AND APPENDAGES. 


TABLE No. 1076. 

Hydrant and Hose Stream Data. Horizontal and Vertical 

Distances of Jets. 




Pressure at Hose Nozzle 

fci N 

W o 

52 

Head, in lbs. per sq. in . 

20 

3 ° 

40 

50 

60 

70 

80 

90 

IOO 

“ “ feet ... 

46.2 

6 9-3 

92.4 

IX 5-5 

138.6 

161.7 

184.8 

207.9 

231.0 


1 Gallons discharged.... 

no 

x 34 

i 55 

173 

189 

205 

219 

232 

245 

i in. 

-< Horizontal Dist. of Jet 

70 

90 

log 

126 

I42 

156 

168 

178 

186 


( Vertical “ “ _ 

43 

62 

79 

94 

108 

121 

* 3 * 

140 

148 


( Gallons discharged. 

J 39 

170 

196 

219 

24O 

259 

2 77 

294 

3 10 

*Ya m. 

Horizontal Dist. of Jet... 

7 i 

93 

113 

132 

148 

163 

175 

186 

193 


(Vertical “ “ .... 

43 

63 

81 

97 

I 12 

125 

137 

148 

157 


1 Gallons discharged. 

171 

210 

242 

271 

297 

320 

342 

363 

383 

iXm. 

•< Horizontal Dist. of Jet 

73 

96 

•us 

138 

156 

I72 

186 

198 

207 


(Vertical “ “ .... 

43 

6 3 

82 

99 

115 

I29 

142 

154 

164 


(Gallons discharged. . . 

207 

253 

293 

327 

358 

387 

4 i 3 

439 

462 

m. 

< Horizontal Dist. of Jet. .. 
(Vertical “ “ . .. 

75 

IOO 

124 

146 

166 

184 

200 

213 

224 


44 

65 

85 

102 

118 

133 

146 

158 

1 _ 

169 


508. Flush Hydrants.—A style of flush hydrant, that 
may be placed under a paved or flagged sidewalk, near the 
edge, is shown in Fig. 122. This style may have one, two, 
or three fixed nozzles. 

Figs. 123 and 124 illustrate a style of hydrant with a 
portable head. This style is manufactured under the 
Lowry patent. It is designed to be placed at the intersec¬ 
tions of mains, in the street, or in the line of a main, but 
may be placed in the sidewalk. In either case it is placed 
within an independent curb, and the cast-iron case rises 
about to the surface. The portable head is of brass and 
composition, nicely finished, as light as is consistent with. 



































Fig. 123 


Fig. 124, 

































































































































































































































522 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


strength, and is usually carried upon the steamer or the 
hose carriage. It has any desired number of nozzles, from 
one to eight, each of which has its independent supplemen¬ 
tary valve. 

In the centre of the portable head is a revolving key that 
operates the main valve stem. 

509. Gate Hydrants.—A variety of metallic “gate” 
hydrants have been introduced, from time to time, and had 
a brief existence, but the majority of them have been soon 
abandoned. The most minute particle of grit upon their 
faces gives trouble, and they are much more likely to stick 
than valves of good sole-leather or of rubber properly pre¬ 
pared, and clamped between metallic plates. Gate hydrants 
of good design and excellent workmanship, should be fully 
successful with filtered water. 

The rubber of valves requires to be very skillfully tem¬ 
pered, or it will be too soft or too hard. It hardens, also, 
as the temperature of the water lowers. 

510. High P ressures.—But a few years since the 
maximum static strain upon hydrants, in public water 
supplies, did not exceed that of a hundred and fifty feet 
head, and the majority of the hydrants in each system had 
not over one hundred feet pressures when the water was at 
rest. Hand or steam fire-engines were necessities in such 
cases, and the pipes were so small that often the engines 
had to exert some suctions on the pipes to draw their full 
supplies. Now the values of pressure that will permit six 
or eight effective streams to be taken direct from the hy¬ 
drants in any part of the system is more fully appreciated, 
and direct pumping pressures equivalent to three or four 
hundred feet head are not uncommon. The effect upon the 
hydrants is, however, a greatly increased strain which they 
must be able to meet. 


AIR-VALVES. 


523 


511. Air-Valves. — All water contains some atmos¬ 
pheric air. When water has passed through a pumping- 
engine into a force-main under great pressure, it absorbs 
some of the air in the air-vessel. If, then, it is forced along 
a pipe having vertical curves and summits at different 
points, it parts w T ith some of the air at those summits. In 
time, sufficient air will accumulate at each summit to oc¬ 
cupy a considerable part of the sectional area at that point, 
and it will continue to accumulate until the velocity of the 
water is sufficient to carry the air forward down the incline. 

At such summits an air-valve is required to let off the 
accumulated air, as occasion requires. Also, when the 
water is drawn off from the pipes, as for repairs or any 
other purpose, there is always a tendency to a vacuum at 
the summits if no air is supplied there ; and if the pipes are 
not thick and rigid, they may collapse in consequence of 
the vacuum strain, or exterior pressure. 

When pipes are being filled, there should always be 
ample escape for the air at the summits, or the air contained 
in the pipes will be compressed and recoil, again be still 
more compressed and again recoil with greater force, shoot¬ 
ing the column of water back and forth in the pipe 'with 
enormous force, and straining every joint. 

In the distribution, hydrants are usually located upon 
summits, and in such case will perform the functions of 
air-valves. 

If a stop-valve is inserted in an inclined pipe, and is 
closed during the filling of the section immediately below it, 
it makes practically a summit at that point, and an air- 
valve or vent will be required there. 

An air and vacuum valve, for summits, may with advan¬ 
tage be combined in the same fixture, the air-valve motion 
being positive in action for the purpose of an air-valve, 


524 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 



opening against tlie pressure, but automatic as a "vacuum- 

valve, opening freely to the pressure ot tlie atmosphere. 

Fig. 125 is a com- 



Fig. 125. bined air and vacuum 

valve designed by the 
writer, and used in sev¬ 
eral cities with success. 

A two-incli air-valve 
answers tolerably for 
four, six, eight, and 
ten inch pipes, but for 
large pipes a special 
branch with stop-valve 
may be used. 

Great care should 
be exercised in filling 
pipes with water, and 
the water should not 
be admitted faster 
than the air can give 
place to it by issue at 
the air-valves, or open 
hydrant nozzles, with¬ 
out reactionary con- 

AIR VALVE. . . 

vulsions. 

512 . Union of High and Low Services. —Many 
cities have high lands within their built-up limits that are 
so much elevated above the general level that it is a matter 
of convenience to divide the distribution into “ high ” and 
“ low services ,” and to give to each its independent reservoir. 

In such case the benefit of the pressure of the high reser¬ 
voir may be secured in the low system in case of a large 
fire, by simply opening a valve in a branch connecting the 



















































































COMBINED RESERVOIR AND DIRECT SYSTEMS. 


two systems. A check-valve, Fig. 126, will be required in 
the effluent pipe, or supply main from the lower reservoir 
to prevent the flow back into the lower reservoir. 

A weighted valve, automatic in action, may also be 
placed in the branch connecting the two systems, and then 

Fig. 126. 



CHECK-VALVE. 

in case of an accident xo the supply pipe of the lower sys¬ 
tem, or a malicious closing of its valve, the upper service 
will maintain the supply at a few pounds diminished 
pressure. 

If the pumps are arranged so as to give a direct increased 
pressure in the lower system for fire purposes, then a check- 
valve in the branch connecting the two systems, opening 
toward the high system, will be an excellent relief and pro¬ 
tection against undue pressure. 

513. Combined Reservoir and Direct Systems.— 
In the plan of a pipe system, Fig. 113, a pipe leads from the 
pumps direct to the reservoir, and a second pipe leads direct 
from the pumps into the distribution, so that water may be 
sent either to the reservoir or to the distribution, at will. 













526 


DISTRIBUTION SYSTEMS, AND APPENDAGES. 


A branch pipe connects these two pipes so as to supply the 
distribution from the force main. 

A check-valve opening toward the distribution is placed 
in this branch. If a fire-pressure is put upon the distribu¬ 
tion through the direct pipe this valve prevents the flow 
back toward the reservoir, but upon the reduction of the 
fire-pressure it comes into action and maintains the supply 
to the distribution from the reservoir. 

For additional security against unforseen contingencies, 
another pipe may lead from the reservoir to one of the prin¬ 
cipal sub-mains, as shown in the plan, when the relative 
positions of the reservoir and distribution permits, and this 
pipe may contain in the effluent chamber a clieck-valve 
against fire-pressure and a weighted relief-valve to prevent 
undue pressure. 

In the reservoir plan, Fig. 58 (page 833), the force and 
supply mains are shown to be connected by a pipe passing 
along the side of the reservoir, so that the water may be sent 
from the pumps direct into the distribution. The supply- 
main has a check-valve in the effluent chamber in this case. 

A combined reservoir and direct pressure system, sub¬ 
stantially like that of Fig. 113, including high and low ser¬ 
vices, was designed by the writer for one of the large New 
England cities in 1872, and the same was constructed with the 
exception of the high service reservoir, in the two following 
seasons. 

514. Stand-Pipes .—Several of the American cities, 
whose reservoirs are distant from their pumping stations, 

I have placed a stand-pipe upon their force-main, to equalize 
the resistance against the pumps, as in St. Louis, Louis¬ 
ville, and Milwaukee. Other cities use tall open-topped 
stand-pipes without reservoirs, when no proper site for a 
reservoir is readily attainable, as at Chicago and Toledo. 

All the American stand-pipes now in use are of the 


FRICTIONAL HEADS IN SERVICE PIPES. 


527 


single leg class. The city of Sandusky, Ohio, has now 
(Nov. 1876) in process of construction a tank stand-pipe of 
25 feet diameter and 208 feet height, surrounding a delivery 
stand-pipe of 3 feet diameter and 225 feet height. This 
tank is being built up of riveted metal plates, from designs 
by J. D. Cook, Esq., chief engineer. In Europe, the stand¬ 
pipes are more frequently double-legged, with connections 
between the up and down legs at intervals of height. 

The stand-pipes as generally used, serve as partial sub¬ 
stitutes for relief-valves combined or acting in conjunction 
with tall and capacious air-chambers. The surface of the 
water in the stand-pipes vibrates up and down according to 
the rate of delivery into them from the pumps, and the rate 
of draught, if the main over which they are placed is con¬ 
nected with the distribution. Vide Chapter XXV, and 
table of stand-pipe data in the Appendix. 

The Boston Highlands Stand-pipe (page 161) stands 
upon an eminence 158 feet above tide, is of wrought-iron, 
and is 80 feet high, and 5 feet interior diameter. It is 
inclosed in a masonry tower. 

The Milwaukee stand-pipe (page 25) rises to 210 feet 
above Lake Michigan, and the Toledo stand-pipe (page 31) 
to 260 feet above Maumee River. 

515. Frictional Heads in Service-Pipes. —The fol¬ 
lowing shows the frictional head in clean, smooth service- 
pipes, with given velocities, for each one-hundred feet length. 

The numbers of the first column are the given velocities., 
in feet per second. The second column gives the head, 
which is necessary to generate the given velocities opposite. 

In the first column, under each of the given diameters 
from J inch to 4 inches, is the volume of flow, at its given 
velocity; in the next column the corresponding coefficient 
of friction ; and in the next column the frictional head per 
each one hundred feet length at its given velocity. 


528 


DISTRIBUTION SYSTEMS, AND APPENDAGES 


Frictional Head 


T 


IN 


ABLE 

Service 

7 >f 9 

n — v 


No. 1 O 

Pipes* (in 


(4 m) 


2 gd 


8 . 

each ioo feet length). 


V 

CD • 


IN. DIAMETER.t 

IN. DIAMETER. 

I IN. 

DIAMETER. 

I Y 2 IN. DIAMETER. 

Velocity, in f 
per second 

Velocity heac 
in teet. 

Cubic feet 
per minute. 

Coefficient. 

Frictional 

head. 

Cubic feet 
per minute. 

Coefficient. 

Frictional 

head. 

Cubic feet 
per minute, 

Coefficient 

Frictional 

head. 

Cubic feet 

per minute. 

| 

Coefficient. 

Frictional 

head. 

1.4 

.030 

• TI 5 

.00992 

Feet. 

3.896 

.257 

.00930 

Feet. 

1.812 

•458 

.00882 

Feet. 

1.289 

1.030 

.00843 

Feet. 

.821 

i.6 

.O4O 

.130 

.00942 

3.592 

•294 

.00890 

2.265 

•523 

.00854 

1.630 

1.178 

.00823 

1.056 

i.8 

.050 

.147 

.00900 

5.355 

•33 1 

.00856 

2.756 

•589 

.00830 

2.005 

I -3 2 5 

.00806 

1.297 

2.0 

.062 

.164 

.00862 

5.136 

.368 

.00830 

3.300 

•654 

.00810 

2.516 

1.472 

.00790 

1.570 

2.2 

•075 

.180 

.00845 

6.091 

•405 

.00811 

3.902 

.719 

.00790 

2.851 

1.619 

.00775 

1.865 

2.4 

.090 

.196 

,00810 

6.950 

•442 

.00792 

5.535 

•785 

.00773 

3.320 

1.766 

.00760 

2,175 

2.6 

.105 

.213 

.00788 

7.935 

•478 

•°°773 

5.193 

•850 

.00758 

3.821 

x-9 I 4 

.00745 

2.520 

2.8 

.122 

.229 

.00770 

8.993 

•5i5 

.00756 

5.891 

.916 

.00745 

5.356 

2.061 

.00730 

2.855 

3-o 

.140 

.246 

.00753 

10.07 

•552 

.00745 

6.665 

.981 

.00734 

5.926 

2.2C>9 

.00722 

3 229 

3-2 

.160 

.262 

.00745 

11.36 

•589 

.00737 

7.501 

1.046 

.00726 

5.555 

2.356 

.00714 

3.635 

3-4 

.180 

.278 

.00736 

12.67 

.626 

.00729 

8.373 

I.II2 

.00720 

6.207 

2-5°3 

.00706 

5.056 

3- 6 

.202 

•295 

.00729 

15.01 

.662 

.007x8 

9.255 

1.177 

.00714 

6.900 

2.651 

.00700 

5.509 

3-8 

.225 

•3 11 

.00726 

15.62 

.699 

.00714 

10.25 

1.243 

.00708 

7.625 

2.798 

.00696 

5.995 

4.0 

.250 

.328 

.00722 

17.21 

•736 

.00710 

11.29 

1.309 

.00702 

8.376 

2-945 

.00692 

5.502 

4.2 

•275 

•344 

.00719 

18.69 

•773 

.00706 

12.38 

1-374 

.00698 

9.182 

3.092 

.00687 

6.022 

4-4 

.302 

.360 

.00715 

20.62 

.810 

.00702 

13.51 

1.440 

.00694 

10.02 

3-239 

.00683 

6.571 

4.6 

•330 

•377 

.007x1 

22.51 

.846 

.00699 

15.70 

1-505 

.00691 

10.90 

3-387 

.00680 

7.159 

4.8 

.360 

•393 

.00708 

25.30 

.883 

.00696 

15.95 

I -57 I 

.00687 

11.80 

3-534 

.00677 

7.751 

5-o 

•39° 

.410 

.00704 

26.22 

.920 

.00693 

17.22 

1.636 

.00684 

12.75 

3.681 

.00675 

8 386 

5-2 

.422 

.426 

.00701 

28.25 

■957 

.00689 

18.52 

1.701 

.00681 

13.73 

3.828 

.00671 

9.017 

5-4 

•455 

•442 

.00698 

30.32 

•993 

.00686 

19.88 

1.767 

.00678 

15.75 

3-975 

.00668 

9.680 

5-6 

.490 

•459 

.00695 

32.57 

1.030 

.00683 

21.29 

1.832 

.00675 

15.79 

4.123 

.00665 

10.37 

5-8 

.525 

•475 

.00692 

35.76 

1.067 

.00680 

22.75 

1.898 

.00672 

16.86 

4.270 

.00662 

11.07 

6.o 

.562 

•492 

.00689 

36.95 

I. IO4 

.00678 

25.26 

i- 9 6 3 

.00670 

17.99 

4.417 

.00660 

11.81 

6.2 

.600 

.508 

.00686 

39.28 

I.I4I 

.00675 

25.79 

2.028 

.00667 

19.12 

4-564 

.00657 

12.55 

6.4 

.640 

•524 

.00683 

51.67 

1.177 

.00672 

27.35 

2.094 

.00664 

20.28 

4.7H 

.00654 

13.31 

6.6 

.680 

• 54 i 

.00681 

hb.OO 

I.214 

.00669 

28.96 

2.159I 

.00661 

21.57 

4-859 

.00652 

15.11 

678 

.722 

•557 

.00678 

5 6.70 

1.251 

.00666 

30.61 

2.225 

.00659 

22.72 

5.006 

.00650 

15.95 

7.0 

•765 

•574 

.00675 

59.27 

1.288 

.00664 

32.35 

2.291 

.00657 

25.01 

5-153 

.00648 

15.78 


* This table does not include the resistances of the stop-cocks and short 
bends in service pipes. Such resistances, as services are usually laid, reduce 
the effective delivery of water fully fifty per cent, 
f Vide table 104 , p. 504 , for values of d in feet. 

\ ide table of weights of lead service pipes in the Appendix. 


















































FRICTIONAL HEAD IN SERVICE PIPES 


529 


TABLE No. 108 — (Continued). 


Frictional Head in Service Pipes (in each ioo feet length). 


^4 

o 

.0) • 


I % IN. DIAMETER. 

2 IN. DIAMETER. 

3 IN - 

DIAMETER. 

4 IN. 

DIAMETER. 

Velocity, in f 
per second 

d 

<D 

4-1 M~< 

|.s 

> 

! Cubic feet 

per minute. 

Coefficient. 

Frictional 

head. 

Cubic feet 
per minute. 

Coefficient. 

Frictional 

head. 

Cubic feet 
per minute. 

Coefficient. 

Frictional 

head. 

Cubic feet 

per minute. 

Coefficient. 

F nctional 
head. 

1.4 

.030 

1.403 

.00800 

Feet. 

.668 

1.875 

.00763 

Feet. 

.557 

4.123 

.00724 

Feet. 

.353 

7-33® 

.00697 

Feet. 

.255 

i.6 

.040 

1.603 

.00786 

.857 

2.142 

.00750 

.715 

4.712 

.00716 

M56 

8.377 

.00690 

,3k2 

i.8 

.050 

1.804 

.00769 

1.062 

2.410 

.00741 

.895 

5-301 

.00708 

.570 

9.424 

.00684 

.kl5 

2.0 

.062 

2.004 

.00757 

1.290 

2.678 

.00731 

1.090 

5.891 

.00700 

.696 

10.47 

.00678 

.505 

2.2 

•075 

2.204 

.00745 

1.536 

2.946 

.00724 

1.306 

6.480 

.00693 

.833 

n.52 

.00672 

.606 

2.4 

.090 

2.405 

.00733 

1.799 

.3.214 

.00717 

1.539 

7.069 

.00687 

.983 

12.56 

.00666 

.715 

2.6 

.105 

2.605 

.00723 

2.083 

3.481 

.00711 

1.791 

7.685 

.00681 

l.lkk 

13.61 

.00660 

.832 

2.8 

.122 

2.806 

.00713 

2.382 

3-794 

.00704 

2.057 

8.247 

.00675 

1.315 

14.66 

.00655 

.957 

3*o 

.140 

3.006 

.00707 

2.711 

4.01S 

.00692 

2.321 

8.846 

.00670 

l.k98 

I 5-7 I 

.00650 

1.090 

3-2 

.160 

3.206 

.00700 

3.05h 

4.286 

.00686 

2.618 

9-435 

.00665 

1.692 

16.76 

.00645 

1.231 

3-4 

.180 

3-407 

.00694 

3.U18 

4-554 

.00681 

2.93k 

10.02 

.00661 

1.899 

17.80 

.00641 

1.381 

3- 6 

.202 

3.607 

.00688 

3.799 

4.821 

.00677 

3.270 

10.61 

.00657 

2.117 

18.85 

.00637 

1.538 

3-8 

.225 

3.808 

.00685 

k.215 

5 -089 

.00674 

3.628 

11.20 

.00654 

2.3k7 

19.90 

.00634 

1.706 

4.0 

.250 

4.008 

.00682 

U.6U9 

5-357 

.00671 

k.002 

11.78 

.00651 

2.588 

20.94 

.00631 

1.882 

4.2 

•275 

4.208 

.00678 

5.096 

5-625 

.00667 

k.385 

I2 -37 

.00647 

2.836 

21.99 

.00628 

2.065 

4-4 

.302 

4.409 

.00674 

5.560 

5-893 

.00663 

k.78k 

12.96 

.00644 

3.098 

23-03 

.00625 

2.255 

4.6 

•33° 

4.6oq 

.00670 

o.oko 

6.160 

.00660 

5.205 

13.55 

.00641 

3.370 

24.08 

.00623 

2.k57 

4.8 

.360 

4.810 

.00667 

6.5U7 

6.428 

.00657 

5.6k3 

14.14 

.00638 

3.653 

25-13 

.00620 

2.662 

5-o 

•39° 

5.010 

.00664 

7.06k 

6.696 

.00654 

6.09k 

14-73 

.00636 

3.951 

26.18 

.00618 

2.880 

5-2 

.422 

5.210 

.00661 

7.615 

6.064 

.00651 

6.561 

I5.3 2 

.00633 

k.253 

27.23 

.00615 

3.099 

5-4 

•455 

5-4 11 

.00658 

8.175 

7.232 

.00648 

7.0kk 

15-91 

.00630 

k.565 

28.27 

.00612 

3.326 

5-6 

•49° 

5.611 

.00655 

8.751 

7-499 

.00645 

7.5kO 

16.50 

.00627 

k.886 

30.32 

.00609 

3.559 

5-8 

•525 

5.812 

.00652 

9.3k5 

7.767 

.00642 

8.0k9 

I 7-°9 

.00624 

5.167 

30-37 

.00607 

3.816 

6 .o 

.562 

6.012 

.00650 

9.970 

8-035 

.0064c 

8.587 

17.67 

.00622 

5.56k 

3i.4i 

.00605 

k.059 

6.2 

.600 

6.212 

.00647 

10.59 

8.303 

.00637 

9.126 

18.25 

.00619 

5.912 

32.46 

.00603 

k.320 

6.4 

.640 

6.413 

.00645 

11.26 

8-57 1 

.00635 

9.69k 

18.85 

.00616 

6.269 

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.00601 

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6.6 

.680 

6.613 

.00643 

11.93 

8.838 

.00633 

10.28 

19.44 

.00614 

6 6k6 

34-55 

.00599 

k.863 

6.8 

.722 

6.814 

.00641 

12.63 

9.106 

.00631 

10.88 

20.03 

.00612 

7.032 

35-6o 

.00597 

5.1k5 

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7.014 

.00639 

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9-374 

.00629 

11.k9 

20.62 

.00610 

7.k27 

36-65 

•00595 

5.k3k 





















































CHAPTER XXIII. 

CLARIFICATION OF WATER. 

516. Rarity of Clear Waters.— A small but favored 
minority of the American cities have the good fortune to 
find an abundant supply of water for their domestic pur¬ 
poses, within their reach, that remains in a desirable state 
of transparency and limpidity. 

The origin and character of the impurities that are 
almost universally found in suspension in large bodies of 
water, have been already discussed in the chapters devoted 
to u Impurities of Water” (Chap. VIII), and to “ Supplies 
from Lakes and Rivers” (Chap. IX) ; so there remains now 
for investigation only the methods of separating the foreign 
matters before pointed out. 

517. Floating’ Debris. —The running rivers, that are 
subject to floods, bring down all manner of floating debris, 
from the fine meadow grasses to huge tree-trunks, and 
buildings entire. These are all visible matters, that remain 
upon the surface of the water, and their separation is 
accomplished by the most simple mechanical devices. 

Coarse and fine racks of iron, and fine screens of woven 
copper wire are effectual intercepters of such matters and 
prevent their entrance into artificial water conduits. 

518. Mineral Sediments. —Next among the visible 
sediments may be classed the gravelly pebbles, sand, disin¬ 
tegrated rock, and loam, that the eddy motions continually 


ORGANIC SEDIMENTS. 


531 


toss up from the channel bottom, and the current bears 
forward. 

These are not intercepted by ordinary screens, but are 
most easily separated from the water by allowing them 
quickly to deposit themselves, in obedience to the law of 
gravitation, in a basin where the waters can remain quietly 
at rest for a time. 

When the water is received into large storage reservoirs, 
it is soon relieved of these heavy sedimentary matters, by 
deposition ; and a season of quietude, even though but a few 
hours in duration, is a valuable preparation for succeeding 
. stages of clarification. 

Next are more subtle mineral impurities, consisting of 
the most minute particles of sand and finely comminuted 
clay, which consume a fortnight or more, while the water is 
at rest in a confining basin, in their leisurely meanderings 
toward the bed of the basin. 

If these mineral grains are to be removed by subsidence 
for a public water supply, the subsidence basin must 
usually be large enough to hold a three-weeks supply, and 
must be narrow and deep, so the winds will stir up but a 
comparatively thin surface stratum, and also so the exposed 
water will not be heated unduly in midsummer. 

510. Organic Sediments. —Next are the organic frag¬ 
ments, including the disintegrating seeds, leaves, and stalks 
of plants, the legs and trunks of insects and Crustacea, and 
the macerated refuse from the mills. 

All these have so nearly the same specific gravity as the 
water, that they remain in suspension until decomposition 
has removed so much of their volatile natures that the 
mineral residues can finally gravitate to the bottom. 

If these are to be removed by subsidence, the basin must 
hold several months supply, at least, and be so formed 


532 


CLARIFICATION OF WATER. 


and protected as to neither generate or receive other im¬ 
purities. 

In addition, are the innumerable throngs of living 
creatures that people the ponds and streams, and their 
spawns. These cannot be removed by subsidence during 
their active existence, and reproduction maintains always 
their numbers good. 

52 0. Organic Solutions. —Still more subtle than all 
the above impurities, that remain in suspension , are the 
dissolved organic matters that the water takes into solution. 
These include the dissolved remains of animate creatures, 
dissolved fertilizers, and dissolved sewage. 

All the former may be treated mechanically with toler¬ 
able success, but the latter pass through the tinest filters 
and yield only to chemical transformations. 

521 . Natural Processes of Clarification.—Nature’s 
process for removing all these impurities, to fit the water 
for the use of animals, is to pass them through the pores of 
the soil and fissures of the rocks. The soil at once removes 
the matters in suspension , and they become food for the 
plants that grow upon the soil, and are by the plants recon¬ 
verted into their original elements. The minerals of the 
soil reconvert the organic matters in solution into other 
combinations and separate them from the water. 

522 . Chemical Processes of Clarification. —Arti¬ 
ficial chemical processes, more or less successful in their 
action, have been employed from the remotest ages to sep¬ 
arate quickly the fine earthy matters from the waters of 
running streams. The dwellers on the banks of streams, 
who had no other water supply, treated them, each for 
themselves, and in like manner have others treated the rain 
waters which they caught upon their roofs, when they had 
no other domestic supplies. 


PROCESSES OF CLARIFICATION. 


533 


Many centuries ago the Egyptians and Indians had dis¬ 
covered that certain bitter vegetable substances which grew 
around them were capable of hastening the clarification of 
the waters of the Nile, Ganges, Indus, and other sediment¬ 
ary streams of their countries. 

The Canadians have long been accustomed to purify 
rain-water by introducing powdered alum and borax, in 
the proportions of 3 ounces of each to one barrel (31J gals.) 
of water; and alum is used by dwellers on the banks of 
the muddy Mississippi to precipitate its clay. Arago ob¬ 
served also the prompt action of alum upon the muddy 
water of the Seine. One part of a solution of alum in fifty 
thousand parts of water results in the production of a floc- 
culent precipitate, which carries down the clayey and 
organic matters in suspension, leaving the water perfectly 
clear. 

Dr. Gunning demonstrated by many experiments that 
the impure waters of the river Maas, near Rotterdam, could 
be fully clarified and rendered fit for the domestic supply 
of the city, by the introduction of .032 gramme of per- 
chloride of iron into one liter of the water. The waters of 
the Maas are very turbid and contain large proportions of 
organic matter, and they often produce in those visitors who 
are not accustomed to their use, diarrhoeas, with other un¬ 
pleasant symptoms. 

Dr. Bischoff, Jr., patented in England, in 1871, a process 
of removing organic matter from water by using a filter of 
spongy iron, prepared by heating hydrated oxide of iron 
with carbon. The water is said to be quite perceptibly 
impregnated with iron by this process, and a copious pre¬ 
cipitate of the hydrated oxide of iron to be afterwards 
separated. 

Horsley’s patent process for the purification of water 


534 


CLARIFICATION OF WATER. 


covers the use of oxalate of potassa, and Clark’s the use of 
caustic lime. 

Mr. Spencer has used in England with great success, in 
connection with sand filtration, the crushed grains of a car¬ 
bide of iron, prepared by roasting red hematite ore, mixed 
with an equal part of sawdust, in an iron retort. This he 
mixes with one of the lower sand strata of a sand filter, and 
its office is to decompose the organic matters in solution in 
the water. The carbide is said to perform its office thor¬ 
oughly several years in succession without renewal. Mr. 
Spencer’s process may be applied on a scale commensurate 
with the wants of the largest cities, and has been adopted 
in several of the cities of Great Britain. 

Dr. Medlock was requested by the Water Company of 
Amsterdam to examine the water gathered by them from 
the Dunes near Haarlem, for delivery in the city. The 
water had a peculiar “ fisli-like” odor, and after standing 
awhile, deposited a reddish-brown sediment. 

Under the microscope, the deposit was seen to consist of 
the filaments of decaying algse, confervas, and other micro¬ 
scopic plants, of various hues, from green through pale- 
yellow, orange, red, brown, dark-brown, to black. 

The Doctor found the open water channels lined with a 
luxuriant growth of aquatic plants, and the channel-bed 
covered with a deposit of black decaying vegetal matter. 
He discovered also that the reddish-brown sediment was 
deposited in greatest abundance about the iron sluice-gates. 
Copper, platinum, and lead, in finely-divided states, were 
known by him to have the power of converting ammonia 
into nitrous acid, and he was led to suspect that iron pos¬ 
sessed the same power. Experiments with iron in various 
states, and finally with sheet-iron, demonstrated that strips 
of iron placed in water containing ammonia, or organic 


CHARCOAL PROCESS. 


535 


matter capable of yielding it, acted almost as energetically 
as the pulverized metal. The organic matters of the Thames 
water in London, and the Rivington Pike water in Liver¬ 
pool, as well as the Dune water in Amsterdam, were found 
to be completely decomposed or thrown down by contact 
wdtli iron, and the iron acted effectually when introduced 
into the water in strips of the sheet metal or in coils of wire. 
This simple and easy use of iron may be employed in sub¬ 
sidence basins or reservoirs on the largest scale for towns, 
as well as on a smaller scale for a single family. 

The results of these experiments with iron were consid¬ 
ered of such great hygienic and national importance by Dr. 
Sheridan Muspratt that he has put an extended account of 
them on record.* 

523. Charcoal Process.— The charcoal plate filters 
prepared under the patent of Messrs. F. H. Atkins & Co., 
of London, have not been introduced here as yet, so far as 
the writer is informed. 

The valuable chemical and mechanical properties of 
animal charcoal for the purification of water have long been 
recognized, and it was the practice in the construction of the 
early English filter-beds, as prepared by Mr. Thom, to mix 
powdered charcoal with the fine sand. 

If there is either lime or iron in the water, as there is in 
most waters, the chemical action results in the formation of 
an insoluble precipitate upon the grains of charcoal, when 
they become of no more value than sand, and their action 
is thenceforth only mechanical. Messrs. Atkins & Co. have 
devised a method of overcoming this difficulty, in part at 
least, by forming the charcoal into plates, usually one foot 
square and three inches thick, and so firm that their coated 
surfaces can be scraped clean. These plates may be set in 


* Muspratt’s Chemistry, p. 1085 , Vol. II. 



536 


CLARIFICATION OF WATER 



Fig. 129. 


CHARCOAL-PLATE FILTERS. 


frames, Fig. 129, as lights of glass are set in a sash, and the 
water be made to How through them. They are compound¬ 
ed for either slower quick filtration; the dense plates (a 
square foot) passing 30 to 40 imperial gallons per diem, the 
porous 80 to 100 gallons, and the very porous 250 to 300 
gallons per diem, when clean. The water may be first 
passed through sand, for the removal of the greater part of 
the organic matters. 

The use of charcoal has heretofore been confined almost 
entirely to the laboratory, so far as relates to the purifica¬ 
tion of water, and animal charcoal has been found very 

«/ 

much superior to wood and peat coals. Its success has 
undoubtedly been due largely to its intermittent use and 
frequent cleanings and opportunities for oxidation. Its 
power of chemical action upon organic matter is very 
quickly reduced, and it must be often cleaned to be 




















































































































































































































































INFILTRATION BASINS. 


537 


effectual. Some very interesting and valuable experiments 
to test the purification powers of charcoal upon foul waters, 
were described to the members of the Institution of Civil 
Engineers, by Edward Byrne, in May, 1867. 

524. Infiltration. —If any water intended for a do¬ 
mestic supply is found to be charged with organic matter 
in solution , the very best plan of treatment, relating to that 
water, is to let it alone, and take the required supply from 

a purer source. 

\ 

The impurities in suspension in water may best be 
treated on Nature’s plan, by which she provides us with the 
sparkling limpid waters of the springs that bubble at the 
bases of the hills and from the fissures in the rocks. 

525. Infiltration Basins. —In the most simple natural 
plan of clarification, a well, or basin, or gallery, is excavated 
in the porous margin of a lake or stream, down to a level 
below the water surface, where the water supply will be 
maintained by infiltration. 

All those streams that have their sources in the mount¬ 
ains, and that flow through the drift formation, transport in 
flood large quantities of coarse sand and the lesser gravel 
pebbles. These are deposited in beds in the convex sides 
of the river bends, and the finer sands are spread upon them 
as the floods subside. From these beds may be obtained 
supplies of water of remarkable clearness and transparency. 

The volume of water to be obtained from such sources 
depends, first, upon the porosity of the sand or gravel be¬ 
tween the well, basin, or gallery, and the main body of 
water, the distance of percolation required, the infiltration 
area of the well or gallery, and the head of water under 
•which the infiltration is maintained. 

A considerable number of American towns and cities 
have already adopted the infiltration system of clarification 


538 


CLARIFICATION OF WATER. 


of their public water supplies, and although it is not one 
that can be universally applied, it should and will meet 
with favor wherever the local circumstances invite its use. 
Attention has not as yet become fairly attracted in America 
to the benefits and the necessities of filtration of domestic 
water supplies, and many of the young cities have been 
obliged to make an herculean effort to secure a public water 
supply, having even the requisite of abundance, and they 
have been obliged to defer to days of greater financial 
strength the additional requisite of clarification. A knowl¬ 
edge of the processes of clarification, which are simple for 
most waters, is being gradually diffused, and this is a sure 
precursor of the more general acceptance of its benefits. 

In some of the small western and middle State towns, 
the infiltration basins have heretofore taken the form of one 
or more circular w T ells, each of as large magnitude as can 
be economically roofed over, or of narrow ojjen basins. In 
the eastern States the form has usually been that of a cov¬ 
ered gallery along the margin of the stream or lake, or of a 
broad open basin. Some of these basins are intended quite 
as much to intercept the flow T of water from the land side 
toward the river as to draw their supplies from the river, 
and the prevailing temperatures and chemical analyses of 
the waters, as compared with the temperatures and analyses 
of the river waters, give evidence, that their supplies are in 
part from the land. 

A thorough examination of the substrata, on the site of 
and in the vicinity of the proposed infiltration basin, down 
to a level eight or ten feet below the bottom of the basin, 
will permit an intelligent opinion to be formed of its percola¬ 
tion capacity. 

526. Examples of Infiltration. —Fig. 130 illustrates 
a section of the infiltration gallery at Lowell, Mass. This 



EXAMPLES OF INFILTRATION. 


539 


gallery is a short distance above the city and above the 
dam of the Locks and Canal Co. in the Merrimac River, 
that supplies some 10,000 liorse-power to the manufacturers 
of the city. The gallery is on the northerly shore of the 
stream, parallel with it, and lies about one hundred feet 
from the shore. 

Its length is 1300 feet, width 8 feet, and clear inside 
height, 8 feet. Its floor is eight feet below the level of the 
crest of the dam. The side walls have an average thickness 
of two and tliree-fourtlis feet, and a height of five feet, and 
are constructed of heavy rubble masonry, laid water-tight 
in hydraulic mortar. 


Fig. 130. 



LOWELL INFILTRATION GALLERY. 


The covering arch is semicircular, of brick, one foot 
thick, and is laid water-tight in cement mortar. 

Along the bottom, at distances of ten feet between 
centres, stone braces one foot square and eight feet long, 
are 

exterior thrust of the earth and the hydrostatic pressure. 





































540 


CLARIFICATION OF WATER. 


The bottom is covered with coarse screened gravel, one foot 
thick, up to the level of the top of the brace stones. 

The Merrimac River is tolerably clear of visible impuri¬ 
ties during a large portion of the year, but during liigln 
water carries a large quantity of clay and of a silicious sand 
of very minute, microscopic grains. 

An inlet pipe, thirty inches in diameter, connects the 
lower end of the gallery directly with the river, for use in 
emergencies, and to supplement the supply temporarily at 
low-water in the river, when it is usually clear. At the ter¬ 
minal chamber of the gallery into which the inlet pipe leads, 
and from which the conduit leads toward the pumps, are 
the requisite regulating gates and screens. 

This gallery w T as completed in 1871, and during the 
drought and low water of the summer of 1873, a test devel¬ 
oped the continuous infiltration capacity of the gallery to 
be one and one-half million gallons per twenty-four hours, 
or about one hundred and fifty gallons for each square foot 
of bottom area per twenty-four hours. 

At Lawrence, Mass., is a similar infiltration gallery along 
the eastern shore of the Merrimac River, from which the. 
city’s supply is at present drawn. 

The infiltration gallery for the supply of the town of 
Brookline, Mass., completed in 1874, lies near the margin 
of the Charles River. The bottom is six feet below the 
lowest stage of water in the river, its breadth between walls 
four feet, and length seven hundred and sixty-two feet. The 
side walls are two feet high, laid without mortar, and the 
covering arch is semicircular, two courses thick, and tight. 

During a pump test of thirty-six hours duration, this 
gallery supplied water at a rate of one and one-half million 

* A considerable percentage of the flow into this and some other infiltration 
basins is judged, from experimental tests, analyses, and temperatures, to be 
intercepted “ ground water ” that was flowing toward the river. 



EXAMPLES OF INFILTRATION. 


54} 


gallons in twenty-four hours, or four hundred and ninety 
gallons per square foot of bottom area per twenty-four 
hours. The ordinary draught up to the present writing is 
about one-third this rate. 

The pioneer American infiltration basins were constructed 
for the city of Newark, N. J., under the direction of Mr. 
Geo. H. Bailey, chief engineer of the Newark water-works. 
These basins are somewhat more than a mile above the 
city, on the bank of the Passaic River. There are two 
basins, each 350 feet long and 150 feet wide, distant about 
200 feet from the river. They are revetted with excellent 
vertical-faced stone walls, and everything pertaining to 
them is substantial and neat. An inlet pipe connects them 
with the river for use as exigencies may require. 

At Waltham, Mass., a basin was excavated from the 
margin of the Charles River back to some distance, and 
then a bank of gravel constructed between it and the river, 
intended to act as a filter. 

The excavation developed a considerable number of 
springs that flowed up through the bottom of the basin, 
and these are supposed to furnish a large share of the 
water supply. 

At Providence, two basins have been excavated, one on 
each side of the Pawtuxet River. These are near the mar¬ 
gin of the River, and are partitioned from the floods by 
artificial gravelly levees. 

At Hamilton and Toronto, in Canada, basins have been 
excavated on the border of Lake Ontario. The Hamilton 
basin has, at the level of low-water in the lake, a water area 
of little more than one acre. 

At Toronto, the infiltration basin lies along the border 
of an island in the lake, nearly opposite to the city. It is 
excavated to a depth of thirteen and one-half feet below 


542 


CLARIFICATION OF WATER. 


low-water in the lake, lias an average bottom width of 26 J 
feet, side slopes 2 to 1, and length, including an arm of 
390 feet, of 3090 feet. This basin is distant about 150 feet 
from the lake. 

The top of the draught conduit, which is four feet diam¬ 
eter, is placed at six and one-half feet below low-water, or 
the zero datum of the lake ; and the water area in the basin, 
if drawn so low as the top of the conduit, will then be 3.75 
acres, and when full to zero line is 5.64 acres, the average 
surface width being then eighty feet. 

During a six days test this basin supplied about four 
and one-quarter million imperial gallons per twenty-four 
hours under an average head of live feet from the lake, or 
at the rate of fifty-two imperial gallons per square foot of 
bottom area per twenty-four hours. 

At Binghamton, Y. Y., two wells of thirty feet diameter 
each, were excavated about 150 feet from the margin of the 
Susquehanna River, one on each side of the pump-liouse. 
These wells are roofed in. 

At Schenectady there is a small gallery along the margin 
of the Mohawk River. 

Columbus opened her works with a basin on the bank 
of the Scioto, and has since added a basin with a process 
of sand filtration. 

Other towns and cities have formed their infiltration 
basins according to their peculiar local circumstances. 

These basins generally clarify the water in a most satis¬ 
factory manner, and accomplish all that can be expected 
l of a mechanical process, but they have not always delivered 
the expected volumes of water; but perhaps too much is 
sometimes anticipated through ignorance of the true nature 
of the soil and false estimate of “ground water” flow. 

527. Practical Considerations.— The experience with 


PRACTICAL CONSIDERATIONS. 


543 


the American and European infiltration basins shows that 
when judiciously located they should supply from 150 to 
200 U. S. gallons per square foot of bottom area in eacli 
twenty-four hours continuously. This requires a rate of 
motion through the gallery inflow surface, of from twenty 
to twenty-five lineal feet per twenty-four hours. 

This inflow is dependent largely upon the area of shore 
surface through which the water tends toward the basin, 
and the cleanliness and porousness of that surface. 

We have not here the aid of Nature’s surface process, in 
which the intercepted sediment is decomposed by plant 
action, and the pores thrown open by frost expansions, but 
are dependent upon floods and littoral currents to clean off 
the sediment separated from the infiltering water. If the 
infiltering surface is not so cleaned periodically by currents, 
it becomes clogged with the sediment, and its capability of 
passing water is greatly reduced. 

A uniform sized grain of sand or gravel offers greater 
percolating facilities than mixed coarse and fine grains. 
The proportion of interstices in uniform grains is from thirty 
to thirty-three per cent, of the bulk, and the larger the grains 
the larger the interstices and the more free the flow. On 
the other hand, the smaller the grains, or the more the ad¬ 
mixture of smaller with predominating grains, the smaller 
the interstices, and the less the flow, but the more thorough 
the clarification and the sooner the pores are silted with 
sediment. 

If there is much fine material mixed with the gravel, 
water will percolate very slowly, and a larger proportional 
infiltration area will be required to deliver a given volume 
of water. 

It will be remembered that we found gravel (§ 351) with 
due admixtures of graded fine materials to make the very 


544 


CLARIFICATION OF WATER. 


best embankment to retain water, even under fifty or more 
feet head. 

The best bank in which to locate an infiltration basin is 
one which is made up of uniform silicious sand grains of 
about the size used for hydraulic mortar, and which has a 
thin covering of finer grains next the body of water to be 
iiltered. The silting will in such case be chiefly in the sur¬ 
face layer, and the cleaning by flood current then be most 
effectual. 

The distance of the basin from the body of water is gov¬ 
erned by the nature of the materials, being greater in coarse 
gravel than in sand. It should be only just sufficient to 
insure thorough clarification when the surface is cleanest. 
A greater distance necessitates a greater expense for greater 
basin area to accomplish a given duty, and a lesser distance 
will not always give thorough clarification. 

The distance should be graduated in a varying stratum, 
so that the work per unit of area shall be as uniform as 
possible. 

528. Examples of European Infiltration.— Mr. Jas. 

P. Kirkwood, C. E., in his report* to the Board of Water 
Commissioners of St. Louis, by whom he w T as commissioned 
to examine the filtering processes practised in Europe, as 
applied to public water supplies, has given most accurate 
and valuable information, which those who are interested in 
the subject of filtration will do well to consult. 

From Mr. Kirkwood’s elaborate report w r e have con¬ 
densed some data relating to European infiltration galleries. 

Perth, in Scotland, has a covered gallery located in an 
island in the River Tay. Its inside width is 4 feet, height 
8 feet, and length 300 feet. Its floor is 2^ feet below low- 
water surface in the river. Its capacity is 200,000 gallons 


* Filtration of River Waters, Van Nostrand, New York, 1869. 



545 


EUROPEAN INFILTRATION. 

per diem, and rate of infiltration per square foot of bottom 
area, 182 gallons per diem. 

Angers, in France, lias a covered gallery located in an 
island in tlie River Loire. This gallery lias two angles of 
slight deflection, dividing it into three sections. The two 
end sections are 3-4" wide and the centre section 6-0" wide. 
The floors of the two end sections are 7J below low-water in 
the river, and of the central section 9J feet below. The 
combined length of these galleries is 288 feet, and their de¬ 
livery 187 gallons per diem per square foot of bottom area. 

These were constructed in 1856, and rest on a clayey 
substratum; consequently the greater part of their inflow 
must be through the open side walls. 

More recently, these have been reinforced by a new 
gallery, with its floor 5J feet below low-water surface in the 
river, and not extending down to the clay stratum. This is 
5 feet wide and 8 feet high, and delivers 300 gallons per 
diem per square foot of bottom area. 

Lyons, in France, has two covered galleries along the 
banks of the Rhone, the first 16 -6" wide and 394 feet long. 
The second is 33 feet wide, except at a short section in the 
centre, where it is narrowed to 8 feet, and is 328 feet long. 
There are also two rectangular covered basins. The com¬ 
bined bottom areas of the two galleries is 17,200 square 
feet, and of the two basins 40,506 square feet. The total 
delivery at the lowest stage of the river is nearly six mil¬ 
lion gallons per diem, or 100 gallons per square foot of 
bottom area. The capacity of the 33-foot gallery alone is, 
however, 147 gallons per square foot of bottom area. About 
6J feet head is required for the delivery of the maximum 
quantity. The average distance of the galleries from the 
river is about 80 feet, and the two basins are behind one of 
the galleries. 

35 


546 


CLARIFICATION OF WATER. 

At Toulouse, France, three covered galleries extend 
along the bank of the Garonne. The first two, after being 
walled, were filled with small stones. 

The new gallery has its side-walls laid in mortar, is cov¬ 
ered with a semicircular arch, is 7 -6 wide, 8-8" high, and 

1180 feet long. Its floor is 8'-7" below low-water surface in 
the river. Its total capacity is a little in excess of mil¬ 
lion gallons, or 228 gallons per diem, per square foot of 
bottom area. 

For the supply of Genoa, in Italy, which lies upon the 
Mediterranean, a gallery has been constructed, in a valley 
of a northern slope of the Maritime Alps, at an altitude of 

1181 feet above the sea. This gallery extends in part 
beneath the bed of the Fiver Scrivia, transversely from side 
to side, and in part along the banks of the stream. The 
width is 5 feet, height 7 to 8 feet, and length 1780 feet. 

The extraordinarily large delivery, per lineal foot, is 
6412 gallons per diem. 

The waters are conveyed down to Genoa in cast-iron 
pipes, with relieving-tanks at intervals. 

529. Example of Intercepting 1 Well. —The great 
well in Prospect Park, Brooklyn, L. I., is a notable instance 
of intercepting basin, such as is sometimes adopted to inter¬ 
cept the flow of the land waters toward a great valley, or 

« 

the sea, or to gather the rainfall upon a great area of sandy 
plain. 

This portion of Long Island is a vast bed of sand, which 
receives into its interstices a large percentage of the rainfall. 
The rain-water then percolates through the sand in steady 
flow toward the ocean. Although the surface of the land 
lias considerable undulation, the subterranean saturation is 
found to take nearly a true plane of inclination toward the 
sea, and this inclination is found by measurements in 


FILTER-BEDS. 


547 


numerous wells to be at the rate of about one foot in 770 ft., 
or seven feet per mile. So if a well is to be dug at one-lialf 
mile from the ocean beach, water is expected to be found 
at a level about three and one-half feet above mean tide ; 
or, if one mile from the beach, at seven feet above mean 
tide, whatever may be the elevation of the land surface. 
If in such subsoils a well is excavated, and a great draught 
of water is pumped, the surface of saturation will take its 
inclination toward the well, and the area of the watershed 
of the well will extend as the water surface in the well is 
lowered. If the well has its water surface lowered so as to 
draw toward it say a share equal to twenty-four inches of 
the annual rainfall on a circle around it of one-quarter mile 
radius, then its yield should be at the rate of very nearly 
one-lialf million gallons of water daily. 

The Prospect Park well, Fig. 131 (p. 102), is 50 ft. in diam¬ 
eter. A brick steen or curb of this diameter, resting upon 
and bolted to a timber shoe, edged with iron, was sunk by 
excavating within and beneath it, fifty-nine feet to the sat¬ 
uration plane, and then a like curb of thirty-five feet diam¬ 
eter was sunk to a further depth of ten feet. The top of the 
inner curb was finished at the line of water surface. A 
platform was then constructed a few feet above the water 
surface, within the large curb, to receive the pumping 
engine. The boilers were placed in an ornate boiler-house 
near the well. 

On test trial, the well was found to yield, after the water 
surface in the well had been drawn down four and one-half 
feet, at the rate of 850,000 gallons per twenty-four hours. 

530. Filter-beds.— A method of filtration, more arti¬ 
ficial than those above described, must in many cases be 
resorted to for the clarification of public water supplies. 

The most simple of the methods that has had thorough 


548 


CLARIFICATION OF WATER. 







S A W 






SAND 


FINE 




C OAR S E': SAND 


kr-tfZ'v* 

I iiVi'V «.*> 


FINE 


> .v v- » 

l^c "O 


y’.V 


r/LW 


DRAIN 


DR A! 


trial, consists in passing the water downward, in an arti¬ 
ficial "basin specially constructed for the purpose, through 
layers of fine sand, coarse sand, fine gravel, coarse gravel, 
and broken stone, to collecting drains placed beneath the 
whole, Fig. 132. 























































































FILTER-BEDS. 


549 


The basins in sncli cases are usually from 100 to 200 
feet wide, and from 200 to 300 feet long, each. Each basin 
is made quite water-tight, the horizontal bottom or floor 
being puddled, if necessary, and sometimes also covered 
with a paving of concrete, or layer of bricks in cement 
mortar. The sides are revetted with masonry, or have 
slopes paved with substantial stone in mortar, or with 
concrete. 

A main drain extends longitudinally through the centre 
of the basin, rests upon the floor, and is about two feet 
wide and three feet high. From the main drain, on eacli 
side, at right-angles, and at distances of about six feet 
between centres, branch the small drains. These are six or 
eight inches in diameter, of porous, or, more generally, per¬ 
forated clay tiles, resting upon the bottom or floor, and they 
extend from the central drain to the side walls, where they 
have vertical, open-topped, ventilating, or air-escape pipes, 
rising to the top of the side walls. 

These pipes and the central drain form an arterial sys¬ 
tem by which water may be gathered uniformly from the 
whole area of the basin. 

This arterial system is then covered, in horizontal layers, 
according to the suitable materials ava^ible, substantially 
as follows, viz.: two feet of broken stone, like “road 
metalone foot of shingle or coarse-screened gravel; one 
foot of pea-sized screened gravel; one foot of coarse sand; 
and a top covering of one and one-half to three feet of fine 
sand. 

This combination is termed a filter-bed , and over it is 
flowed the water to be clarified. 

Provision is made for flowing on the water so as not to 
disturb the 'fine sand surface. This inflow duct is often 
arranged in the form of a tight channel on the top of the 


550 


CLARIFICATION OF WATER. 


covering of tlie central gathering drain, and the water flows 
over its side walls, during the filling of the basin, to right 


and left, with slow motion. 

The depth of water maintained upon the filter-bed is 
four feet or more, according to exposure and climatic effects 
upon it. 

At the outflow end of the central gathering drain is an 
effluent chamber, with a regulating gate over which the 
filtered water flow^s into the conduit leading to the dear- 
water basin. The water in the effluent chamber is connected 
with the water upon the filter-bed through the drains and 
interstices of the bed ; consequently, if there is no draught, 
its surface has the same level as that upon the bed, but if 
there is draught, the surface in the chamber is lowest, and 
the difference of level is the head under which water flow r s 
through the filter-bed to the effluent chamber. 

The regulating gate in the effluent chamber controls the 
outflow there to the clarified water basin, and consequently 
the head under which filtration takes place, and the rate of 
flow through the filter-bed. 


531. Settling and Clear-water Basins. —When the 
water is received from a river subject to the roil of floods, it 
should be received first into a settling basin , where it will 
be at rest forty-eight hours or more, so that as much as 
possible of the sediment may be separated by the gravity 
process, before alluded to. Its rest in large storage basins 
prepares it very fully for introduction to the filter-bed, 
which is to complete the separation of the microscopic 
plants, vegetable fibres, and animate organisms, that can¬ 
not be separated by precipitation. 

Since the domestic consumption of the water at some 
hours of the day is nearly or quite double the average con¬ 
sumption per diem, the clarified water basin should be 


FILTER-BED SYSTEM. 


551 


large enough to supply the irregular draught and permit 
the flow through the filter to he uniform. 

This system of clarification in perfection includes three 
divisions, viz. : the Settling Basin , the Filter-bed, and the 
Clear-water Basin. 

The settling and clear-water basins may be constructed 
according to the methods and principles already discussed 
for distributing reservoirs (Chap. XVI). The capacity of 
each should be sufficient to hold not less than two days 
supply, and the depth of water should be not less than 
ten feet, so that the water may not be raised to too high 
a temperature in summer, and that its temperature may 
be raised somewhat in winter before it enters the distribu¬ 
tion-pipes. 

532. Introduction of Filter-bed System.— Pough¬ 
keepsie, on the Hudson, was the first American city to 
adopt the filter-bed system of clarification of her public 
water-supply. 

The Poughkeepsie works were constructed in 1871, to 
take water from the Hudson River. During the spring 
floods, the river is quite turbid. These filtering works con¬ 
sist of a small settling basin and two filter-beds, each 73J ft. 
wide and 200 ft. long. Each bed is composed of 

24 inches of fine sand. 

6 “ “ pinch gravel. 

6 “ “ pinch gravel. 

6 “ “ i-inch broken stone. 

24 “ “ 4 to 8-inch spalls. 

72 “ total. 


The floors on which the beds rest are of concrete, twelve 
inches thick. 

The clear-water basin is 28 by 88 feet in plan, and 17 ft. 
deep. 



552 


CLARIFICATION OF WATER. 


Water is lifted from the river to the settling basin by a 
pump, and it flows from the dear-water basin to the suction 
chamber of the main pump, giving some back pressure. 
From thence it is pumped to the distributing reservoir. 

The filter-beds are at present used but a portion of the 
year, subsidence in the main reservoir being sufficient to 
render the water acceptable to the consumers. 

In the recent construction of the new water supply for 
the city of Toledo, 20,000 square feet of filter-bed was at 
first prepared to test its efficiency in the clarification of the 
turbid Maumee River water. The great demand for water 
has, however, made the construction of additional filter area 
and large subsidence basins a necessity, the consumption 
having already (1876) reached nearly 3,000,000 gallons per 
diem. Anticipating the necessity, Chief Engineer Cook has 
devised and is experimenting with a series of chambers, to 
contain filtering materials through which the water is to be 
flowed with an upward current. 

When our American water consumers are more familiar 
with this filter-bed system of clarification, now in such gen¬ 
eral use in England and Scotland and on the Continent, its 
use will be oftener demanded. Subsidence, as we have 
before remarked, does not completely clarify the water, 
even in a fortnight’s or three weeks’ time, but a good sand 
filter, if not overworked, intercepts not only the visible sedi¬ 
ment and fine clay, but the most minute vegetable fibres 
and organisms and the spawn of fish, and it is highly im¬ 
portant that these should be separated before the water is 
passed to the consumer. 

533. Capacity of Filter-Beds.— Experience indicates 
that the flow through a filter-bed, such as we have above 
described, should not exceed the rate of 17 feet lineal per 
diem, or be reduced by silting of the sand layer to less than 


CLEANING OF FILTER-BEDS. 


553 


8.5 feet per diem. It must not be so rapid as to suck the 
sand grains or clay particles or the intercepted fibres 
through the bed, or its whole purpose will be entirely 
defeated. 

A rate of about one-lialf inch per hour, or twelve lineal 
feet per diem, when the filter is tolerably clean, is generally 
considered the best. This gives the filter-bed a capacity of 
twelve cubic feet, or 89.76 gallons, per square foot of sur¬ 
face per twenty-four hours, and requires, in work, about 
12,000 square feet of filtering surface for each million gal¬ 
lons of water to be filtered per diem. 

534. Cleaning of Filter-Beds.— The filter-beds upon 
the English streams require cleaning about once a week, 
when the rivers are in their most turbid condition, and 
ordinarily once in three or four weeks. 

The process of cleaning consists of removing a slice of 
about one-lialf inch thickness from the surface of the fine 
sand layer, and the stirring or loosening up of the sand that 
is packed hard by the weight of the water, when the clog¬ 
ging of the filter prevents or hinders greatly its flow. This 
requires the water to be drawn off from the bed to be cleaned, 
and of course puts the portion of filter area being cleaned 
out of service. According to the usual practice, the water is 
drawn down only about a foot below the sand surface for 
the cleaning ; but there is a great advantage, though an in¬ 
convenience, in drawing the water entirely out of the bed, 
for this admits the air to oxidize the organic matters that 
are drawn into the filter, which is of great importance. 

To provide for cleaning, the required area for service 
should be divided into two or more independent beds, and 
then one additional bed should be provided also, so that 
there shall always be one bed surplus that may be put out 
of use for cleaning. 


554 


CLARIFICATION OF WATER. 


The greater the number of equal divisions the less will 
be the surplus area to be provided, and on the other hand, 
each division adds something to the cost, so that both con¬ 
venience and finance are factors controlling the design as 
well as the form and extent of lands available. 

As a suggestion merely, it is remarked that the divisions 
may be approximately as follows, for given volumes, de¬ 
pendent on the turbidness of water and local circumstances : 


TABLE No. 109. 

Dimensions of Filter-Beds for Given Volumes. 

For i million gallons per diem, 3 beds 60 feet x 100 feet. 


ft 

2 

ft 

ft 

H 

3 

if 

80 

ft 

X 

150 

ft 

tt 

3 

tt 

it 

it 

3 

if 

100 

tt 

X 

180 

it 

tt 

4 j 

tt 

it 

tt 

4 

it 

100 

tt 

X 

180 

tt 

a 

6 

it 

ti 

ft 

4 

ft 

100 

ft 

X 

240 

tt 

tt 

8 

tl 

it 

it 

4 

it 

120 

tt 

X 

270 

a 

tt 

10 

if 

it 

ft 

5 

it 

120 

ft 

X 

270 

tt 


535. Renewal of Sand Surface. —When thd repeated 
parings from the surface have reduced the top fine-sand 
layer to about twelve inches thickness, a new coat should 
be put on restoring it to its original thickness. 

If good fine sand is difficult of procurement, the pairings 
may perhaps be washed for replacing with economical 
result. 

This is sometimes accomplished by -letting water flow 
over the sand in an inclined trough of plank, having cleats 
across it to intercept the sand, or by letting water flow up 
through it in a wood or iron tank. In the latter case water 
is admitted under pressure through the bottom of the tank, 
and the sand rests upon a grating covered with a fine wire 
cloth, placed a short distance above the bottom of the tank. 
The current is allowed to flow up through the sand and over 
the top of the tank until it runs clear. 


BASIN COVERINGS. 


555 


53G. Basin Covering's.— The British and Continental 

w V 

filter-beds are rarely roofed in, although the practice is 
almost universal of vaulting over the distributing reservoirs 
that are near the towns. 

The intensity of our summer heat and intensity of winter 
cold in our northern and eastern States, makes the roofing 
in of our filter-beds almost a necessity, though we are not 
aware that this has been done as yet in any instance. 

The use of the shallow depth of four feet of water, so 
common in the English filters, would be most fatal to open 
filters here, for the water would frequently be raised in 
summer to temperatures above 80° Fall, and sent into the 
pipes altogether too warm, with scarce any beneficial 
change before it reached the consumer. Such tempera¬ 
tures induce also a prolific growth of algce upon the sides 
of the basin, and upon the sand surface when it has become 
partially clogged, and soon produce a vegetable scum upon 
• the water surface also. As these vegetations are rapidly 
reproduced aud are short-lived, their gases of decomposi¬ 
tion permeate the whole flow, and render the water ob¬ 
noxious. 

Depth of water and protection from the direct heating 
action of the sun are the remedies and preventatives for 
such troubles. A free circulation of air and light must, 
however, be provided, and also the most convenient facili¬ 
ties for the cleansing and renewal of the bed. 

In Fig. 132 is presented a suggestion for a roof-covering 
that will give the necessary protection from sun and frost, and 
the requisite light, ventilation, and convenience of access. 

The side walls are here proposed to be of brick, and the 
truss supporting the roof to be of the suspended trapezoidal 
class. The confined air in the hollow walls, and the saw¬ 
dust or tan layer over the truss, are the non-conductors that 


556 


CLARIFICATION OF WATER. 


assist in maintaining an even temperature within the basin, 
and resist the effects of intense heat and intense cold. 

The Parisian reservoirs at Memlmontant, and the splen¬ 
did new structure at Moutrouge, are covered with a system 
of vaulting, after the manner practised by the Romans, and 
this system is also followed by the British engineers in their 
basin covers. 

A substantial cover over a filter basin will reduce the 
difficulties with ice to a minimum, and remove the risk of 
the bed being frozen while the water is drawn off for clean¬ 
ing in winter. In such case, if the water is drawn imme¬ 
diately from a deep natural lake, or a large impounding 
reservoir, the only ice formation will be a mere skimming 
over of the surface in the severest weather, and the inflow 
of water, at a temperature slightly above freezing, will tend 
constantly to preserve the surface of the water uncongealed, 
and the sand free from anchor ice. 


Fig. 133 . 



PUMPING ENGINE No. 3, BROOKLYN. 




























































































































































































































































































































CHAPTER XXIV. 


PUMPING OF WATER 

537. Types of Pumps. —The machines that have Ibeen 
used for raising water for public water supplies in the United 
States present a variety of combinations, but their water 
ends may be classified and illustrated by a few type forms. 

Our space will not permit a discussion of the theories 
and details of their prime movers, nor more than a general 
discussion of the details of the pumps, with their relations 
to the flow of water in their force mains. 

The horizontal double-acting piston pump of the type, 
Fig. 134, is an ancient device, and in its present form re¬ 
mains substantially as devised by La Hire, and described 
in the Memoirs of the French Academy in 1716. This was 
at one time a favorite type, and was adopted for the most 
prominent of the early American pumping works, as at 
Philadelphia, Richmond, New Haven, Cincinnati, Mon¬ 
treal, etc. 

Several modifications of the vertical plunger pump, after 
the modern Cornish pattern (Fig. 135), were later intro¬ 
duced at Jersey City, Cleveland, Philadelphia, Louisville, 
etc., and in 1875 at Providence. 

The vertical bucket pump (Fig. 133), in various modifi¬ 
cations (referring to the water end only), was introduced at 
Hartford, Brooklyn, New Bedford, etc. 

The bucket-plunger pump (Fig. 136, water end), has 
been more recently introduced at Chicago, St. Louis, Mil¬ 
waukee, Lowell, Lynn, Lawrence, Manchester, etc. 


558 


PUMPS. 


A vertical acting differential plunger pump, having one 
set of suction and one set of delivery valves, each arranged 
in an annular ring around the plunger chamber, has re¬ 
cently been invented by at least two engineers, independ¬ 
ently of each other, and with similar disposition of parts. 
This, like the bucket and plunger pump, is single-acting in 
suction and double-acting in delivery. This pump gives 
promise of superior excellence 

The double-acting horizontal plunger pump (page 223), 
itself an ancient and admirable invention, was first intro¬ 
duced in combination with the Worthington duplex engine 
about the year 1860, and has since been adopted at Harris¬ 
burg, Charlestown, Newark, Salem, Baltimore, Toledo, 
Toronto, Montreal, etc. 


Fig. 134. 



Rotary, and gangs of small piston pumps have been in¬ 
troduced to some extent, in direct pressure systems, in some 
of the small Western towns. 
























































EXPENSE OF VARIABLE DELIVERY OF WATER. 559 


538. Several of tlie earliest pumps * of magnitude worthy 
of note were driven by overshot, or breast water-wheels, as 
at Bethlehem, Pa., Fairmount Works, Philadelphia, New 
Haven, Richmond, and Montreal. Turbines have, how¬ 
ever, taken the places of the horizontal wheels at Phila¬ 
delphia and Richmond, and in part at Montreal, and tur¬ 
bines give the motion at Manchester, Lancaster, Bangor, 
and at other cities. 

Fig. 143 shows the latest improved form of the G-eyelin- 
Jonval turbine, which has been used very successfully in 
several of the large cities for driving pumps. 

The greater number of the pumping machines now in 
use are actuated by compound steam-engines. 

A considerable number of the large pumping machines 
have their pump cylinders in line with their steam cylin¬ 
ders, and their pump rods in prolongation of their steam 
piston rods. 

539. Expense of Variable Delivery of Water.— 

It is important that the delivery of water into the force-main 
from the pumping machinery be as uniform as possible, 
and constant. 

If the delivery of water is intermittent or variable, and 
the flow in the main equally variable, then power is con¬ 
sumed at each stroke in accelerating the flow from the 
minimum to the maximum rate. 

The ms mr>a\ of the column of water in the force-main, 
surrendered during the retardation at each stroke, is neutral- 

* Bethlehem, Pa., constructed in 1762 the first public water supply in the 
United States in which the pumps were driven by water-power. Philadelphia 
constructed, in 1797, on the Schuylkill River, a little below Fairmount, the 
first public water-works in the United States driven by steam-power. In 1812 
steam-pumps were started at Fairmount, and the old works abandoned. In 
April, 1822, the hydraulic-power pumps were started at Fairmount. 

f Vide “ principle of vis viva,” in Moseley’s “ Mechanics of Engineering:,” 
p. 115, New York, 1860, and Poncelet’s Mecanique Industrielle, Art. 135, 
Paris, 1841. 




560 


PUMPS. 


ized by gravity, and no useful effect or aid to the piston of 
the pump is given back, as useful work is given during the 
retardation of the fly-wheel of an engine. 

If, as when the pump is single-acting, motion is gener¬ 
ated during each forward stroke, and the column comes to 
rest during the return stroke of the piston, or between 
strokes of the piston, the power consumed (neglecting fric¬ 
tion) to generate the maximum rate of motion, equals the 
product of the weight of the column of water into the height 
to which such maximum rate of motion would be due if the 
column was falling freely, in vacuo, in obedience to the in¬ 
fluence of gravity. 

Let Q be the volume of water to be set in motion, in 
cubic feet, w the weight of a cubic foot of water, in pounds 
(= 62.5 lbs), h x the equivalent height, in feet, to which the 


rate of motion is due ), and p l the power required to 

produce the acceleration ; then 

Pi = Q x w x h x . (1) 


If the velocity is checked and then accelerated during 
each stroke, without coming to a rest, let v be the maximum 
velocity, in feet per second, and the minimum velocity; 
then the power consumed in or necessary to produce the 
acceleration is 

P> = Qxvx \^-Tg[ & 


In illustration of this last equation, which represents a 
smaller loss than the first, assume the force-main, with air- 
vessel inoperative, to be 1000 feet long and 2 feet diameter, 
and the maximum and minimum velocities of flow to be 
5 feet and 4 feet per second respectively. 

The weight of the contents of the main into its accelera¬ 
tion will be (.7854cZ 2 x Z) x w x -I -- - i = 3142 cu. ft. x 

(2g 2g) 





EXPENSE OF VARIABLE DELIVERY OF WATER. 561 


62.5 lbs. x .14 ft. = 27492.5 foot-lbs. If there are ten strokes 
per minute, 274925 foot lbs. = 8J HP will be thus con¬ 
sumed. If the main is twice, or four times as long, the 
power consumed will be doubled, or quadrupled. 

The power required to accelerate the motion of the 
column is in addition to the dynamic power P Y in foot-lbs., 
required to lift it through the height //, of actual lift. 

For the equation of lifting power per second, when Q is 
the volume per second (neglecting friction), we have 

Pi = Q x w x H, (3) 

or for any time, 

P 1 = QxtxwxH. (4) 


The frictional resistance to How in a straight main is 
proportional, very nearly to the square of the velocity of 
flow (to mv 2 ), and is computed by some formula for frictional 
head 7i'\ among which for lengths exceeding 1000 feet is 


h" = 


4 Imp 
2gd ’ 


( 5 ) 


in which IP is the vertical height, in feet, equivalent to the 

frictional resistance. 

I “ length of main, in feet. 
d “ diameter of the main, in feet. 
m is a coefficient, which may be selected from 
Table 61, page 242, of values of m. 


The equation of power p", to overcome the frictional 
head, is 


„ ^ 4 Imv 2 

p = Q XWXwr . 


( 6 ) 


The equation of power required, expressed in horse¬ 
powers [HP.] of 33,000 foot-pounds per minute, each, for 
dynamic lift, and frictional resistance to flow combined, is 


Q x t x w x (H+ h") 

[^' • J “ 33,000 


(7) 


36 






562 


PUMPS. 


The several resistances above described are all loads 
upon the pump-piston, and their sum, together with the 
frictions at angles and contractions, is the load, from the 
flow in the main which the prime mover has to overcome. 

When the delivery of the water into the main is constant 
and uniform, these resistances are at then* minimum. 

540. Variable Motions of a Piston. —If we analyze 
the rates of motion during the forward stroke of a piston 
moved by a revolving crank with uniform motion, whose* 
length or radius of circle is 1 foot, we find the spaces or dis¬ 
tances moved through in equal times by the piston, while 
the crank-pin passes through equal arcs, to be as in the fol¬ 
lowing table. 

TABLE No. HO. 


Piston Spaces, for Equal Successive Arcs of Crank Motion, ii^°. 


Arcs. 

Space, ft.. 

O 

O 

o 

O 

.0223 

O 

22 J- 
.0648 

O 

33* 

• io 34 

O 

45 

.1384 

0 

.1655 

O 

6 75 

.1849 

O 

78?- 

.1946 

O 

90 

.1981 


o 

0 

O 

0 

O 

0 

O 

O 


Arcs. 

IOl£ 

112^ 

123^ 

135 

14 6-i- 

1575 

i68| 

180 

.... 

Space, ft. . 

. 1921 

. 1806 

. 1609 

•1375 

.1104 

.0814 

.0488 

.0163 

.... 


The spaces are equal to the above, but in inverse order 
during the return stroke. To compute spaces for other 
lengths of crank, and the same arcs, multiply the given 
lengths of crank in feet by the above spaces. 

The sum of the motions of the piston while the pin moves 
through the first 90° is 1.072 feet, and while through the 
second 90° is .928 feet; therefore the motion of the piston 
is faster during the first and fourth parts of the revolution 
than during the second and third. 

The motion of the piston is accelerated through .5218 of 
its forward and .4782 of its return stroke, and is retarded 
during the remaining parts of its forward and backward 





























Fig. 135 



CORNISH PUMP, JERSEY CITY 































































































































































































































564 


PUMPS. 


motions; and with the usual length of connecting rod, it 
attains a maximum velocity equal to about 1.625 times its 
mean velocity. 

If the pump is single acting, then no delivery of water 
takes place during the return stroke, and this is the most dif¬ 
ficult case of intermittent motion to provide for in the main. 

541. Ratios of Variable Delivery of Water.—If we 
analyze the ratios of movement of a single, and the sums of 
ratios of movement of two or three coupled double-acting 
pump pistons, when the two crank-pins are 90 apart, and the 
three pins 60°, we find the ratios, during the forward motion 
of piston No. 1, for given arcs, approximately as in the 
following table: 

TABLE No. 111. 


Ratios, and Sums of Ratios, of Piston Motions for Equal 
Successive Arcs of Crank Motion, iiJ 0 . 



O 

0 

O 

O 

O 

O 

O 

O 

0 

Arcs. 

O 

II? 

22^ 

33 ? 

45 

56? 

6 7 i 

OO 

90 

i piston. 

•o 

.0423 

.0840 

.1180 

.1490 

• 1653 

.1906 

.1967 

.1953 

2 pistons. 

.1629 

.2293 

•2550 

.2697 

•2753 

.2730 

.2567 

.2366 

.i960 

3 pistons. 

.3426 

• 37 °° 

.3866 

.3896 

•3776 

•3577 

.364° 

•3853 

•393° 


O 

O 

O 

O 

O 

O 

O 

0 


Arcs. 

IOI^ 

II 2 J 

123 ? 

135 

146? 

157 ^ 

H 

ON 

OO 

*>!» 

180 


i piston. 

•1853 

.1710 

.1500 

.1250 

.0967 

.0660 

•0333 

.O 


2 pistons. 

.2293 

.2546 

.2680 

.2730 

.2730 

.2610 

.2310 

.i960 

• • • • 

3 pistons. 

.3810 

• 3 6 I 3 

.3200 

•3777 

•3893 

•3856 

• 37 °° 

•3740 

.... 


The variations of motion, and of delivery of water , on 
each side of the mean rate of delivery is with one piston 
about 10 per cent., with two pistons about 5| per cent., and 
with three pistons about per cent., or in other words, the 
ratios of excess of delivery are .10, .055, .025, and the ratios 
of deficiency have like values. 

542. Office of Stand-Pipe and Air-Vessel. —It is 
the office of the stand-pipe and air-vessel to take up the 






















































CAPACITIES OF AIR-VESSELS. 


565 


excess, and to compensate for the deficiency of delivery by 
the pump pistons, plungers, or buckets. These are most 
effective when nearest to the pump cylinders. 

The excess of delivery enters the open-topped stand-pipe 
and raises its column of water, and the column is drawn 
from and falls to supply the deficiency. Work is expended 
to lift the column, and this work is given to the advancing 
water in the main when the column falls again, but when 
the piston is again accelerated it has the labor of checking 
the motion of the falling column in the stand-pipe. 

The air-vessel on the force main is practically a shorter, 
closed-top stand-pipe containing an imprisoned body of 
air. The excess of delivery of water from the pumps enters 
the air-vessel and compresses the air, and the expansion of 
the air forces out water to supply the deficiency. The reduc¬ 
tion at each stroke of the mean volume of the air in the 
vessel is directly proportioned to the excess of water deliv¬ 
ered and received into the air-vessel, which is, for different 
pumps, proportional to their variations, or if coupled or 
working through the same air-vessel, to the algebraical 
sums of their variations. 

543. Capacities of Air-Vessels. —The cubical capa¬ 
city of an air-vessel for one pair of double-acting pumps is 
usually about five or six times the combined cubical capa¬ 
city of the water cylinders ; but we shall see that the capa¬ 
city of the cylinders alone is not the full basis on which the 
capacity of the vessel is to be proportioned. 

If the air-vessel is filled with air under the pressure of 
the atmosphere only, and then is subjected to a greater 
pressure of water, it will not remain full of air, for the air 
will be compressed, and, according to Mariotte’s law,* its 


* Vide Lardner’s Hydrostatics and Pneumatics, p. 158. London, 1874. 




566 


PUMPS. 


volume will be inversely proportional to the pressure under 
which it exists, provided the temperature remains the same. 
Thus, if the vessel was tilled under a pressure of 15 lbs. per 
square inch, and the water pressure is six times greater or 
00 lbs. per square inch, and the temperature is unchanged, 
then the air-vessel will be but one-sixth full. 

It is the reduced volume of air in the vessel that is com¬ 
pressed to take up the excess of water delivered by the 
pumps ; therefore the degree of pressure should be a factor 
in the equation of capacity of air-vessel, as well as the ratio 
of excess of delivery during a half stroke. 

Let q be the volume of delivery of a pump piston dur¬ 
ing its forward stroke, r the ratio of excess; or if two or 
more pistons are coupled, the algebraic sum of ratios of 
excess of delivery of water during the forward stroke of 
No. 1 piston, n the maximum pressure of water in atmos¬ 
pheres 14.7 lbs. per square inch each), and f an experi¬ 
ence coefficient wdiose value will ordinarily be about 15, 
then the equation for cubical capacity, (7, in cubic feet, of 
air-vessel is, 

C=qxrxnxf 9 (8) 

or if p is the maximum water pressure, in pounds per square 
inch, then the equation, when f — 15, may take the form 

C = pqr . (9) 

If the water is to be permitted to abstract an appreciable 
portion of the air from the air-vessel, that is, if the air-vessel 
is not to be frequently recharged, then the coefficient in the 
above equation should be greater than 15. If the air-vessel 
is to be recharged often, mechanically, with volumes of air 
greater than the atmospheric pressure would supply, then 
the coefficient may be some less than 15. 




Fig. 136. 



LYNN PUMPING ENGINE. — (E. D. Leavitt, Jr.’s, Patent.) 









































































































568 


PUMPS. 


The larger the water surface in contact with the air in 
the air-vessel, the faster the air is absorbed by the water; 
therefore it is advisable to give considerable height in pro¬ 
portion to diameter to the air-vessel, and a disk of wood or 
other nearly or quite impervious material, one or two inches 
less in diameter than the air-vessel, may be allowed to lie 
on the water in the vessel, and thus still more reduce the 
surfaces of contact of air and water. 

544. Valves.—Pumps that have to lift water to heights 
greater than thirty feet, are usually of necessity, or for 
convenience of access, placed between the water to be 
raised and the point of delivery. When so situated they 
perform two distinct operations, one of which is to draw the 
water to them, and the other to force it up to the desired 
elevation. When the pump piston or plunger advances, 


Fig. 137 . 



the water in front of it is pressed forward, and at the same 
time the pressure of the atmosphere forces in water to fill 
the space or vacuum that it w r ould otherwise leave behind 
it. The return of the water must be prevented, or the work 
done by lifting it will be wasted. Valves which open freely 
to forward motion of the water and close against its return, 
are, therefore, a necessity, both upon the suction and the 
delivery sides of the pump. 

All valves break up and distort, in some degree, the ad¬ 
vancing column of water. Such distortions and divisions 






VALVES. 


569 


cause frictional resistance, which consumes power. The 
valve that admits the passage of the column of water by or 
through it with the least division or deflection from its direct 
course, neutralizes least of the motive power. Short bends 
and contractions in water jiassages, that consume a great 
deal of power or equivalent head, often occur in their Avorst 
degree in pump valves. 

The piston valve which moves entirely out of the water- 
passage, and permits the flow of water in a single cylindrical 
column, such for instance as was used in the Darlington 
and Junker water-engines,* is perhaps least objectionable 
in the matter of frictional resistance to the moving water, 
but is often inconvenient to use. The single flap-valve 
(Fig. 137), with area at 30° lift exceeding the sectional area 
of the pump cylinder, gives also a minimum amount of fric¬ 
tional resistance. 

The single annular form of column, while passing through 
the vaTve, is less objectionable than any of the other divi¬ 
sions of the water, and annular valve openings have been 
the favorite forms in nearly all the large pumping ma¬ 
chines. 

In some of the earlier pumps the suction was through a 
single valve with two annular openings, after the Harvey 
and West model, or, as more familiarly known, the Cornish 
double-beat valve, similar to Fig. 138, illustrating the valves 
used in the Brooklyn engines. 

When pumps began to be built of great magnitude, 
requiring large capacities for flow, and the valves Avere 
increased in size to two feet diameter and upward, the 
valves were found to strike very powerful blows as they 


* Vide illustration of a water-engine in Rankine’s “Steam Engine,” p. 140, 
London, 1873, and Lardner’s Hydrostatics and Pneumatics, p. 312. London, 

1874. 




570 pumps. 

Fig. 138. 



came upon their seats, and to make the whole machine, the 
building, and the earth around the foundations tremble. 

This annoyance led to dividing the valves into nests of 
five or more valves of similar double-beat form. In London 
and other large English cities the valves have of late been 
of the four-beat class, or Husband’s model. 

In many pumps the valves have of late been divided into 
nests of twelve or more rubber-disks (Fig. 139) in each set, 
seating upon grated openings in a fiat valve-plate. Each 
subdivision increases the frictional resistance, but reduces 
the force of the blow, or waler-liammer , when the valve 
strikes its seat. 

The suction and delivery valves of the piston pumps 
(Fig. 134) were usually of the flap or hinged pattern. These 
piston-pumps had sometimes, though rarely, their cylinders 
placed vertically, as at the Centre Square Works erected in 




















































MOTION OP WATER THROUGH PUMPS. 


571 


Philadelphia in 1801, and at the Schuylkill Works erected 
in the same city in 1844. They were inclined ten or twelve 
degrees from the horizontal at Montreal. 

The horizontal plunger, 
or “Worthington” pumps 
(page 223), have uniformly 
keen fitted with nests of rub¬ 
ber disk valves. 

The best of the modern 
steam fire-engines are fitted 
with nests of rubber disk 
valves, showing that this 
class of valve is a favorite 
when the pressure is great and the motion is rapid. 

The rubber disk valve (Fig. 139) was sketched from an 
Amoskeag fire-steamer valve. 

545. Motion of Water Through Pumps. —Water is 
so heavy and inelastic that large columns of it cannot be 
quickly started or stopped, without the exertion or opposi¬ 
tion of great power to overcome its inertia, or ms viva. 
There is therefore an advantage, as respects the even and 
moderate consumption of power, when the piston or plunger 
motion is reciprocal, in making the strokes long, and few 
per minute. 

The case is entirely different with an elastic fluid like 
steam. The tendency of the most successful modern steam 
engineering has been toward quick strokes- and high steam 
pressures, and with high degrees of expansion in the larger 
engines. 

The “indoor” ends of the beams of the best Cornish 
pumping-engines are longer than the “outdoor” ends, and 
it is claimed as one of their special advantages that the in¬ 
door or steam stroke that lifts the plunger pole can be made 


Fig. 139. 

































572 


PUMPS. 


with rapidity, while the outdoor stroke, or fall of the 
plunger by its own weight, can be gradual, and thus the 
water be pressed forward at a nearly steady and uniform 
rate. The single-cylinder, single-acting, non-rotative Cor¬ 
nish engine is admirably adapted to the work to which 
it was early applied by Watt and Boulton—namely, the 
raising of water from the deep pits of mines by suc¬ 
cessive lifts to the surface adits, where it flowed freely 
away ; but when applied to long force-mains of water- 
supplies, a stand-pipe near the pump becomes a necessity 
to neutralize the straining and laborious effects of the inter¬ 
mittent action. 

54G. Double-Acting* Pumping-Engines. —The de¬ 
sire to overcome the objectionable intermittent delivery of 
the single-acting pump, as well as the influence of the sharp 
competition among engine-builders, that forced them to 
study methods of economizing the first cost of the machines 
while maintaining their capacity and economy of action, 
led to the introduction, for water-supply pumping, of the 
compound or double cylinder, double-acting, rotative or 
fly-wheel engine. This last class of engines was brought to 
a high state of perfection by Mr. Wicksted and Mr. Simp¬ 
son at the London pumping stations. Some admirable 
pumping machines of this class have been constructed for 
American water-works from designs of Messrs. Wright, 
Cregeir, Leavitt, and others. 

547. Geared Pumping-Engines. —Geared compound 
pumping-engines, one style of which (the Nagle) is shown in 
side and end elevations* in Figs. 140 (p. 377) and 141 (p. 573), 
are well adapted both for direct pumping, and also where 
the reservoir and direct systems are combined. Advantage 

* From the design adopted for the Providence High Service, and working 
with direct pressure. 







GEARED PUMPING ENGINE. 






PLAN. — J. T. Fanning, C. E. 

















































































































































Fig. 141. 





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u,..o / a a & s e 7 8 i /* — -a /a /& /f 

.. -- 1 - - - .- 1 -■— j 


CROSS SECTIONAL ELEVATION. 


NAGLE’S 


GEARED PUMPING ENGINE. 























































































































































































































574 


PUMPS. 


may liere be taken of high pressure of steam, rapid steam 
piston stroke, and large degree of steam expansion, while 
the water piston moves relatively slow with a minimum 
number of reversals. 

548. Costs of Pumping’ Water.—The following table 
(p. 575) gives the running expenses for pumping water in 
various cities. 

549. Duty of Pumping Engines. —The duty or 
effective work of a steam pumping-engine, as now usually 
expressed, is the ratio of the product, in foot-pounds, of 
the weight of water into the height it is lifted, to one hun¬ 
dred pounds of the coal burned to lift the water. 

This standard is an outgrowth from that established 
by Watt, about the year 1780, for the purpose of compar¬ 
ing the performances of pumping-engines in the Cornish 
mines, when Messrs. Boulton and Watt first introduced 
their improved pumping-engines upon condition that their 
compensation was to be derived from a share of the saving 
in fuel. Watt first used a bushel of coal as the unit of 
measure of fuel, equal to about 94 pounds, and afterward 
a cwt. of coal, equal to 112 pounds. More recently, in 
European practice, and generally in American practice, 
100 pounds of coal is the unit of measure of fuel. In some 
recent refined experiments, the weight of ashes and clinkers 
is deducted, and the unit of measure of fuel is the combus¬ 
tible portion of 100 pounds of coal. The use of these sev¬ 
eral units, differing but slightly from each other in value, 
leads to confusion or apparent wide discrepancies in results, 
when the performances of different pumping-engines are 
compared, unless the results are all reduced to an uniform 
standard. 

To construct an equation in conformity with the more 
generally accepted standard of duty, let Q be the volume 


GEARED PUMPING ENGINE. 





SIDE ELEVATION.—J- T. Fanning, 





















































































































































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NAGLES GEARED PUMPING ENGINE 

















































































































































































TABLE No. 112. 

Cost of Pumping, per Million Gallons, in Various Cities, in 187 ^. 


COSTS OF PUMPING WATER. 


575 


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H HM M CO>- 

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576 


PUMPS. 


of water delivered in any given time into the force-main, in 
gallons; w the weight* of a gallon of water in pounds 
(=8.34 lbs. approximately); H the dynamic height of lift; 
h the height equivalent to the frictional resistance between 
pumps and reservoir, including resistances of flow, valves, 
bends, etc., in the force-main, but not the work due to in¬ 
termittent motion of pumps, or to bends and frictions within 
the pump itself; W the weight, in pounds, of coal passed 
into the furnace in the given time ; and D the duty per 100 
pounds of coal; then 

r, _ Q x w x {H + 7i) /1AX 

. 01 W ' K; 


Sometimes the value of Q is expressed in cubic feet, in 
which case w is the weight in pounds of a cubic foot of 
water (= 62.33 lbs. approximately). 

If it is preferred to use the area of plunger, its mean rate 
of motion in the given time, and the pressure against which 
it moves, as factors in the calculation, then the equivalent 
equation of duty takes the form, 

n _ cA x V x t x (P + p) 

.01 W ’ 1 ' 

in which A is the area, in square feet, of the piston or 
bucket, and c its coefficient of effective delivery, which 
varies from .60 to .98, according to design or condition of 
the valves and velocity of flow through them ; V the mean 
rate of motion, in feet per minute, of the plunger or bucket; 
t the given time, in minutes; P the pressure, in pounds, 
due to the dynamic head ; the pressure in pounds due to 
the resistances in the force-main ; and W the weight of 


* Vide Table 38 for weights of water per cubic foot, at different temperatures. 







DUTY OF PUMPING ENGINES. 


577 


coal, in pounds, passed into the furnace in the given 
time. 

If W is taken for denominator in the equation instead of 
.01 If 7 , then the result gives the duty per pound of coal. 

The numerator in each equation refers to the foot-pounds 
of work done by the plunger or bucket of the pump in effec¬ 
tive delivery of water into and efflux from the force-main, 
and the denominator refers to the foot-pounds of work con¬ 
verted from the heat in the coal, and effectively applied by 
the combination of boiler and steam engine. 

The coefficient c and the terms li and p in equations 10 
and 11 are ordinarily appreciably variable with variable 
rates of plunger or bucket motion. Preliminary to a general 
duty test of a pump the values of c for different velocities 
or rates of piston motion, from minimum to maximum, 
should be determined by a reliable and accurate weight or 
weir test, and the value of li or p be accurately determined 
for similar conditions by an accurate gauge or pressure test, 
and a scale, per unit of velocity prepared for each, so that 
values may be read off for the actual rates of piston motion 
during the general test. 

The main parts or divisions which make up a steam 
pumping engine, are: 

1. Boilers (including grates, heating surfaces, steam and 
water spaces, and flues). 

2. Steam engine (including steam pipes, cylinders, valves, 
pistons, and condensing apparatus). 

3. Pump (including water passages, cylinders, plunger 
or bucket, and valves). 

In comparisons of data, for the selection or design of the 
parts of such a combination, the classes of each part should 
be considered in detail, independently, with prime costs, 


37 


578 


PUMPS. 


since if either part gives a low duty alone, the duty pf the 
combination will suffer in consequence. 

Attention will be given especially to the evaporative 
power of the boiler and its duty, or ratio of effective to 
theoretical pressure delivered into the steam pipe; the effec¬ 
tive piston pressure capabilities or duty of the steam cylin¬ 
der, over and above its condensations, enhanced by slow 
motion, leakages of steam, and frictions ; and the frictional 
resistances of the pump piston or plunger, and valves, and 
reactions in the water passages. 

Each pound of good coal, according to the dynamic 
theory of heat, contains in its combustible part about 14,000 
heat units, which are developed into a force by the burning 
of the coal to produce steam, and this force is capable of 
performing a definite amount of work. From sixteen to 
twenty per cent, of these heat units are, ordinarily, lost by 
escape up the chimney; sixteen to twenty per cent addi¬ 
tional are lost by condensation of the steam in the pipes 
and cylinders, and by leakage past the piston or valves into 
the condenser, and about fifty per cent, of their equivalents 
escape with the exhaust steam into the condenser. Only 
about ten or twelve per cent, of these heat units are ordi¬ 
narily transformed into actual useful work done by the 
steam. 

If the engine has many rubbing surfaces, or binds at 
any bearing, or if the pumps have crooked water passages, 
many divisions of the jet in the valves, frequent and rapid 
startings and checkings of the water column, or if its binds 
at any bearing, then each of these resistances consume a 
portion of the remaining ten or twelve per cent, of useful 
work of the steam. 

Stability and substantiality are matters of the utmost 
importance to be considered in the selection of a class or 


ECONOMY OF A HIGH DUTY. 


579 


manufacture of pumping engines. By these terms, in this 
connection, we mean the capability of endurance of contin¬ 
uous action at the standard rate and work, without stoppage 
for repairs, and with the minimum expenditure for repairs. 

This power of continuous work at a maximum rate is of 
far greater value, ordinarily, than an extremely high duty, 
if stability is sacrificed in part for the attainment of a high 
duty, for the comfort and safety of the city may be jeopard¬ 
ized by a weakness in its pumping engine. Stability being 
first attained, then duty becomes an element of excellence 
and superiority. 

Fig 142. 



geyelin’s duplex-jonval turbine (r. d. WOOD & CO., PHILA.) 


550. Special Trial Duties.— The following table (page 
580) gives the duty results obtained by special trials of 
various engines, under the direction of experts.* 

551. Economy of a High Duty.— The financial value 

of a high duty is too often overlooked._ 

* Vide report of Messrs. Low, Roberts and Bogart; in Journal of American 
Society of Civil Engineers. Vol. IV, p. 142. 










































































































































580 


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55 

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a 

55 

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THREE-CYLINDER TUBULAR BOILER. 

NEWPORT, R. I., WATER WORKS. 

[Constructed for George II. Norman, Proprietor. 





£ 


FRONT ELEVATION. — J. T. Fanning's Patent. 

















































































































































































































































































THREE-CYLINDER TUBULAR BOILER. 
Newport, R. I., Water Works. 





SIDE ELEVATION. —J. T. Fanning’s Patent. 



























































































































































































































































































































































COSTS OF PUMPING WATER. 


581 


Engines of substantial construction can now be readily 
obtained, that, when working continuously at their stand¬ 
ard capacities, will give duties of from 75 to 100 million 
foot-pounds per 100 pounds of coal. When they are real¬ 
izing less than their maximum duties, money, or its equiva¬ 
lent, goes to waste. 

We have just seen (§ 549) that duty is a ratio of effec¬ 
tive work. If we divide the dynamic work to be done by 
this ratio, then we have the pounds of coal required to do 
the work when the given duty is realized. 

Let I) be the given duty in foot-pounds per* 100 pounds 
of coal; Q the volume of water delivered into the force-main 
in gallons; w the weight of a gallon of water, in pounds 
(= 8.34 lbs., approximately); H the actual height of lift; 
li the height equivalent to the frictional resistances in the 
main ; and W the weight of coal required, in pounds ; then 
we have for equation of weight of coal, 

w _ 100$ x w x (H 4- 7i) 

When Q and D are in even millions, the computation 
will be shortened by taking one million as the unit for those 
quantities. 

Let us assume that we have one million gallons of water 
to lift 100 feet high in twenty-four hours, then the pounds 
of coal required at various duties will be approximately 
as follows: 


TABLE No. 1 14. 

Comparative Consumptions of Coal at Different Duties. 


Duty, in millions. 

105 

100 

95 

90 

85 

80 

75 

70 

Pounds of coal. 

794 

834 

878 

9 2 7 

981 

1042 

1112 

1191 

Duty, in millions. 

65 

60 

55 

5 ° 

45 

40 

30 

20 

Pounds of coal. 

1283 

1390 

1516 

1668 

1853 

2085 

2780 

4170 































582 


PUMPS. 


The relative costs per annum, in dollars, for lifting 
various quantities of water daily 100 feet high, at different 
duties, will be approximately as in the following table, 
on the assumption that the coal costs $8 per ton of 2000 
pounds, when delivered into the furnace. 

TABLE No. 115. 


Fuel Expenses for Pumping, Compared on Duty Bases. 


Duty in 
millions of 

Number of millions of gallons pumped daily, one hundred teet high. 

(Coal in furnace at $8 per ton.) 

foot-pounds. 









1 

2 

3 

4 

6 

8 

IO 



Cost of coal per annum , 

in dollars. 



IOO 

$1277.86 

$2556 

$3834 

$5IH 

$7667 

$10223 

$12779 

9° 

1419-85 

2840 

4260 

5679 

8519 

H359 

14198 

So 

1597-32 

3195 

4792 

6389 

9584 

12778 

15973 

70 

1825.51 

3651 

5477 

7302 

IO953 

14604 

18255 

6o 

2129.76 

4260 

6389 

8519 

I2779 

17038 

21298 

50 

2555-72 

5III 

7667 

IO223 

15334 

20446 

25557 

40 

3I94-65 

6389 

9584 

12769 

19168 

25537 

31946 

30 

4259-53 

8519 

12779 

17038 

25557 

34076 

42595 

20 

6389.30 

12768 

19168 

25537 

39336 

5H74 

63893 


If the lift is 150 feet, then the annual cost will be one 
and one-half times the above amounts respectively, if 200 
feet, twice the above amounts, etc. 

If we have four million gallons per day to pump 100 feet 
high, then the cost of coal per annum for a 100 million 
duty engine will be about $5000, and with a 20 million duty 
engine about $25000. If we have to pump the same water 
200 feet, the coal for the first engine will cost about $10,200 
and with the second engine $51,000. These sums capital¬ 
ized represent the relative financial values of the engines, 
so far as relates to cost of fuel. 

If pumping-engines are sufficiently strong, of good me¬ 
chanical workmanship, and simple in arrangement of parts, 
then the cost of attendance, lubricants, and ordinary re¬ 
pairs, while doing a given work, will be substantially the 



















COSTS OF PUMPING WATER. 


583 


same for different makes or designs. Beyond this the rela¬ 
tive merits of machines of equal stability, independent of 
prime cost, are nearly in the inverse order of the amount of 
fuel they require to do a given work. 

But the first costs of the complete combination should 
be made a factor in the comparison, including costs of foun¬ 
dations and extra costs of buildings, standpipes, etc., if re¬ 
quired, as in the case of Cornish engines. Then the relative 
economic merits are inversely as the products of costs into 
reciprocals of duties, or directly as duty divided by cost. 

Let C d be the cost in dollars of the complete pumping- 
engine, including foundations, pump-wells, etc., and D the 
duty in millions, then the most economic engine, so far as 
relates to cost of fuel, will be that which has the least 


product of C d x 



or 


C d 

D’ 


and the relative result will be very 


nearly the same if the cost of engine is capitalized. 

Let % be the per cent., or rate of interest at which the 
cost is capitalized, then the most economic engine, as to 
prime cost and duty, will be that which has the least pro¬ 


duct of ^ x 

% 


1 1 

- TO or 
D % 


x 


ft 

D‘ 


Let us assume that we have five million gallons of water 
to lift 100 feet high per day, and that a standard engine of 
suitable capacity to do the work, realizing one hundred mil¬ 
lion duty, will cost $65,000. 

With this standard let us compare, financially, engines 
of less first cost and giving less duties, as in the following 
table, in which the ratio of the standard is taken equal 
unity. 


584 


PUMPS. 


TABLE No. 116. 

Comparison of Values of Pumping-Engines of Various Prime 

Costs and Duties on Fuel Bases. 


Cost = Q. 

Duty = D . 

~ X Cd 

C , x — =-• 

d D D 

Ratio. 

$65,000 

IOO M. 

650.0 

I. 

60,000 

90 “ 

666.6 

I.025 

50,000 

75 “ 

666.6 

I.025 

45,ooo 

60 “ 

750.0 

I-I 53 

35 > 000 

50 “ 

700.0 

I.077 

25,000 

30 “ 

833-3 

1.282 


By the column of ratios in the table we learn that the 
$25,000 engine will really cost twenty-eight per cent, more 
per annum than the $65,000 engine, for the same work, and 
that the purchase of the assumed standard engine, if it has 
stability equal to that of the lower-priced engine, will lead 
to the most profitable results. 

In the table, the $50,000 pumping-engine giving a seventy- 
five million duty, is seen to have a financial value almost 
identical with that of the assumed standard engine. If it 
is also freer from liability to breakage or interruption, if it 
requires less labor or less skill in attendance, if it is easier 
in adjustment to varying work when variable work is to 
be performed, or if it is better adapted mechanically to the 
special work to be performed, then the practical over¬ 
balances the financial advantages, and it is obviously en¬ 
titled to preference in the selection, and good judgment will 
lead to the purchase of this rather than of the assumed 
standard engine. 



















TANK STAND-PIPE, SOUTH A KINGTON WATER WORKS, 


MASS, 

To face p. 585 . 





















































































CHAPTER XXV. 


TANK STAND-PIPES. 

552. Tlieir Function. —Many municipalities are sit¬ 
uated in slightly undulating districts, where elevated, 
embanked, or masonry reservoirs, of capacity to hold a 
supply of water equal to five or six days’ draught of the 
town, or more, are unattainable. In such places, the 
metallic tank stand-pipe, or water-tower, located on some 
moderate elevation, or raised on a trestle, or masonry tower, 
becomes a valuable adjunct to the water system, and espe¬ 
cially so to the systems of the smaller towns and villages, 
where its capacity ought always to equal a full day’s con¬ 
sumption of water. 

The tank stand-pipe has great value in connection with 
steam pumping plants unconnected with a large elevated 
reservoir, when compared with direct pressure alone, for a 
steam boiler cannot so promptly respond with increased 
pressure to a demand for a large increase of flow at the 
hydrants, as can the water power of the usual hydraulic 
pumping plant. The ready filled elevated tank may save a 
delay in increased volume and pressure of water that saves 
also one-half the town from destruction by fire. 

An efficient hydrant stream delivers approximately two 
hundred gallons of water per minute, and a 24x100 feet 
tank, holding a quarter of a million gallons of water, would 
supply five such streams four hours, or would contain the 
daily supply of fifty gallons each for five thousand persons, 
and if its base was sufficiently elevated would allow of the 


586 


TANK STAND-PIPES. 


daily pumping for three thousand persons to be performed 
in about ten hours of each day, which would give favorable 
stoppages of all the machinery for inspections, cleanings 
and repairs, and might cover many contingencies. For 
instance, a pumping machine might so break as to destroy 
its mate, a boiler might burst so as to destroy the whole 
battery, the pump house might burn or be blown up, a 
break in the force main might do serious injury to the 
pump house, the machinery, its duplicate main, etc. ; thus 
the tank may save its cost in one day, and it is a perpetual 
protector. For many reasons, their use is becoming gen¬ 
eral where the larger reservoirs are impossible. 


553. Foundations. —An excellent class of masonry is 
necessary for tall stand-pipe foundations, because the 
resultant pressures, xy, Fig. 143, from the great weight of 
water, combined with the wind force upon the tank, or its 
inclosing superstructure, often has its direction near to the 
edge, or outside the base of the metal shell, and severe 
pressures are thus thrown upon the outside edge of the 
foundation. The wrenching action of the winds under such 
conditions tends to movements and disintegrations of the 
masonry. 

In good coursed masonry with strong cement mortar, 
such pressures should be kept within limits as follows : 


Concrete masonry, 55 lbs. per sq. in. 
Brickwork “ 70 “ “ “ 

Sandstone “ 104 “ “ “ 

Granite “ 140 “ “ “ 


4 tons per sq. foot. 


5 

7-5 

10 


u 

u 

u 


u 

u 


u 


u 

u 

u 


\ 


The foundation should be sufficiently broad, so that the 
direction of the greatest resultant of weight and wind will 
cut the base within one-fourtli diameter distance from its 
centre. 


TENDENCY TO SLIDE. 


587 


554. Wind Strains. — Tornadoes attack uninclosed 
stand-pipes witli the most destructive forces they have to 
withstand. 

The severe forces of the wind are to be considered in 
determining their materials, thicknesses and anchorages. 

When the uninclosed tank is empty, it is least stable 
against wind forces, as respects horizontal sliding and ten¬ 
dency to overturn. 

Wind pressure upon the curved surface of one semi- 
circumference of a vertical cylindrical tank may be consid¬ 
ered as acting upon an infinite series of equal tangential 
surfaces surrounding the curve, and the ratio of effect of 
the force in the direction of the centre of the curve will, on 
each tangent, equal the cosine of the interior included angle 
between the tangent and direction of the wind. The mean 
of the series of cosines thus developed is .70711 + , and the 
resultant effect of the sum of forces in a direction parallel 
with the general motion of the wind is as the square of this 
mean cosine, or .5. The sum of the series of cosines equals 
the diameter of the cylinder. We may, therefore, consider 
the force of the wind as acting upon the diametrical plane 
of the tank, which is perpendicular to the direction of the 
wind, with .5 its normal force, or if the tank is octagonal 
with .79 its normal force, and if the tank is square, with 
its full normal force. In severe gales, the normal force of 
the wind is sometimes 40 pounds per square foot. 

555. Tendency to Slide. — Tanks as usually con¬ 
structed have not sufficient weight, when empty, to resist 
the tendency to a sliding motion when a very strong wind 
is pressing on them. 

If we assume the extreme force of the wind on a plane 
at right angles to its direction as 40 pounds = P per square 
foot, and consider P as acting on the diametrical plane A 


588 


TANK STAND-PIPES. 


= diameter d into height H oi tank, and the ratio of effect 
equal .5, then we have the total distributed force of the 
wind W upon the tank, Fig. 148, 

W= MPdII = MPA. (1) 

If the tank is not bolted or anchored in some manner to 
the foundation, its resistance to sliding motion equals its 
total weight M into its coefficient 2 of friction (mean coef. 
about .25); hence the product zM — must be greater 
than MPA , or the tank must be anchored in position. 

55G. Tendency to Overturn. — Tank stand-pipes 
that are relatively tall usually lack stability against ten¬ 
dency to overturning when a very strong wind is pressing 
on them. 

We have in the last section found the total pressure of 
wind on a plain vertical cylindrical tank to be 

W = MPA. 

This pressure is distributed over an entire semi-circum¬ 
ference of the tank, but for computation of its effect we 
may consider its centre of pressure and resultant as acting 
upon the centre of gravity of the vertical diametrical plane 
which, in the plain tank of equal diameter throughout its 
height, is at the centre of height, = J//; therefore the lev¬ 
erage action in such case equals and the moment of 
wind force W x , tending to overturn the tank, equals 

W x = (MPA) x — MHW. (2) 

If there are external cornices, ornaments or stairways, 
their wind resultants must be computed and included 
in W x . 

The moment of resistance M x of the empty tank to the 
moment of wind force equals its total weight, M, into the 
resisting leverage of one-half the diameter of the base. 



TENDENCY TO OVERTURN. 


589 


M x — \dM ; (3) 

hence, the moment M y — ,5dM must be greater than the 
moment = .5i7TF, or the tank must be anchored in 
position. 

Table No. 117 illustrates these wind and weight effects 
on emx>ty tanks. 


TABLE No. 117. 
Tank Stabilities of Position. 


(.P — 40 lbs. per sq ft., d — diam. in ft., H = height in ft.) 


Diameter. 

Height. 

Weight of Tank 

M. 

Wind Pressure 

2000 

• 

>> 

2 

a 

c/i q 

1 11 

2 'Sb° 

3 ^ 

U 

Leverage Moment of 
W eight. 

M , — .$ dM . 

Leverage Moment of 
Wind. 

IV, = .5 HW . 

Weight of Anchorage. 

* _ (TsH) + b*lV „ 

• 

2 

U-> 

1 

Feet. 

Tons. 

Tons. 

Tons 

Tons. 

Tons. 

Tons. 


IO X IOO 

l6. 

IO 

4 

80. 

5 00 

M 

O 

00 

0 

15 X IOO 

3 i -5 

I 5 

7-875 

236.25 

75 ° 

9 °-S 

20 X IOO 

45 - 

20 

11.250 

45 °* 

. 1000 

75 - 

0 

25 X 100 

80.5 

2 5 

20.125 

1006.25 

1 25° 

37-5 

30 X 100 

112.8 

3 ° 

28.200 

1692. 

1500 

3 - 

2 


When the leverage moment of wind TFi on the empty 
tank exceeds the leverage moment of weight M x , the 
deficiency is covered by bolting the base of the tank to its 
foundation. 

The weight of anchorage, B , clasped by the bolts should 
be not less than 



(MH) + bx W 
.5d 




in which b equals the depth the bolts extend into the 
masonry foundation. This gives a small coefficient of safety 
as the foundation semi-diameter exceeds the tank semi- 
diameter. If D equals the diameter of the foundation, 






















590 


TANK STAND-PIPES. 


then .25D may be substituted for .5d as the divisor in the 
equation of B. 

557. Tank Materials.—In metal tank construction 
there is much that is parallel with good boiler manufacture, 
but the tanks are not, in use, subjected to the blistering 
effects of hot furnace gases, or to so great a range of expan¬ 
sion and contraction. 

Tall stand-pipes, that are not inclosed, are subject to 
intense pressure strains tending to tear open their vertical 
joints, and intense leverage strains tending to tear open 
horizontal joints near their bases. 

A portion of the upper section of the tank of medium or 
small diameter requires only a thin sheet of metal to with¬ 
stand the pressure of the water alone, but a surplus of 
metal is usually necessary near the top, to give the desired 
rigidity, and in many cases to resist the strain from ice 
that may form on the surface of the water when it is quiet. 
Sheets of lower sections have more pressure strain and 
require a better quality of material, while the lower sheets 
of tall pipes demand all the best qualities of first class iron 
or steel boiler plates, and should be thoroughly inspected 
as to thickness, tensile strength, and ductility, and be free 
from “cold-short” or brittle qualities. 

A weight * test of each sheet is a convenient check on 
the accuracy of the gauge test of thickness, and the usual 
cold bend tests along and across the grain give, in the most 
simple manner, indications of the imperative qualities of 
toughness and ductility of the plates and rivets. 

For reliable comparative tests of ultimate tensile resist¬ 
ance, limit of elasticity and uniformity of texture, resort is 
had to a testing machine adapted to such experiments. 


* Vide Table No. 100, page 488, for weights of metal plates. 






RIVETING. 


591 


Metals used for high pressures should be selected from 
plates that have been branded with the name of the manu¬ 
facturers and tensile strength. 

Internal laminations in thick plates of iron or puddled 
steel, caused by imperfect welds under the rolls ; internal 
porous strata of cinder or sand, and internal blisters may 
elude detection only by careful tapping hammer tests. 

Some careful experiments have been made to ascertain 
the comparative resistances of iron and steel to rust, when 
in contact with water, and the advantage was found to be 
slightly with the iron, therefore the reduction of thickness 
of steel plates for a given strength may be offset by the 
weakening effects of oxidation. 

558. Riveting. —As plates are always weakest along 
the lines of rivet holes, their additional thicknesses to give 
joints the required strengths will be considered, or included 
in the magnitude of the factor of safety, when adjusting 
their proportions. 

In punching plates, the holes are laid out, so far as pos¬ 
sible, to retain at least seventy per cent, of the area of the 
sheet along the punched section, and on the other hand the 
rivets are as large as necessary to limit the pressure on the 
rivet bearing of the punched hole to 15000 pounds per 
square inch of “ bearing area,” so called, which is found by 
taking product of diameter of hole into thickness of plate. 

Yarious experiments show the relative strengths of riv¬ 
eted joints in one-half inch plates to have mean values of 
the full strength of the plates about as follows : 

Strength of unpunched plate. i.oo 

“ “ single riveted lap joint. 56 

“ “ double “ “ 70 

“ “ “ “ single welt joint.. .65 

“ “ “ “ double welt joint. .78 





5 92 


TANK STAND-PIPES. 


These percentages are slightly greater in thinner and 
slightly less in thicker plates. 

Double riveting of the vertical lap joints saves an addi¬ 
tion of from twelve to fifteen per cent, to the thickness of 
the plates, to cover weakness of joints under heavy pressure 
of water, and the butt joint with double covering plate gives 
a slight additional saving. 

The rivets in the lower horizontal joints of tall stand¬ 
pipes will be relieved of much shearing strain if the joints 
are butted and covered with double welt plates. The mean 
ultimate shearing strength of each rivet is about three- 
fourths its ultimate tensile resistance. 

The entire lap of a single riveted joint is about three 
times and of a double riveted joint about five times the 
diameter of the rivet, while the width of the covering plate 
for a double-riveted joint is nine or ten diameters of the 
rivet. 

The covering plates for single riveted joints should be 
slightly thicker than the tank plates they cover. 

Those plates subject to great pressure should have their 
edges planed so that the calking may be more uniform and 
reliable, 

Table No. 118 will give data of joints subject to consid¬ 
erable pressure. 


TABLE No. 118. 
Pitch and Sizes of Rivets. 


Thickness of Plates, j 

.2500 

• 3 I2 5 

■3750 

• 4375 

.5000 

• 5625 

.6250 

.6875 

.7500 

OO 

M 

N 

Ln 

0 

m 

rv 

00 

•9375 

I 

inches. ) 

M 

5 

1 0 

% 

7 

10 

l / 2 

0 

1 0 

% 

IX 

% 

13 

% 

15 

I 

Diameter of Rivets, j 

X 



% 

% 

% 

% 


1 Pa 


inches. j 

% 

Tif 

% 

I 

I 

I 


Length of Rivets, j 
inches. f 

1 % 

*T« 

US 

2 

2 % 

2t« 

2T B o 

2U 

3 

3X 

3*4 

3 t« 

3 tt 

Pitch in single | 

riveted joints, j 
Pitch in double / 


2% 

2 M 

2 i 4 

2 V2 

2>4 

2 \ 

2% 

2% 

2^ 

2& 


2/4 

2)4 

riveted joints. $ 

2% 

2% 

3l4 

3^ 

3% 

3% 

3 % 




























JONVAL TURBINE. 

Constructed by R. D. Wood & Co., Philadelphia. 






































































































































FACTORS OF SAFETY. 


593 


559. Pressures in Inclosed Stand-Pipes.— In a 

tank containing water, and protected from the forces of the 
winds, the bursting pressure p of the water per square 
inch on the interior surface of the tank shell is directly as 
the head h of water on the given inch, and in pounds per 
square inch equals 

p — ASAti. (5) 

The theoretical thickness t of the circular metal sheet at 
any given depth from full water surface may be computed 
by the formula heretofore given (§ 446, p. 448) for cylindri¬ 
cal shells, viz. : 

t = ~ X/, (6) 



in which t = thickness of metal sheet, in inches. 

p = pressure, for given depth 7^, in pounds per 
sq. in. 

r — radius of cylindrical shell, in inches. 
s — ultimate cohesion of metal used, in lbs. per 
sq. in. 

f — factor of safety adopted. 

* 

5GO. Factors of Safety. —In tall stand-pipes the risk 
of rupture in the joints increases more rapidly with depth 
below water surface than the ratio of thickness of metal, 
due to pressure alone ; hence the coefficient should increase 
with the depth, say from 3 or 4 for twenty-five feet depth 
to 6 or 7 for one hundred and fifty feet depth. 

The increase of the factor of safety, /, may follow nearly 
as the eleventh root of the fourth power of the depth, 
whence, 


/ = h* 


(8) 


£>94 


TANK STAND-PIPES. 


Several values of f thus obtained are given in Table 
No. 119, for the formula 

, fv 

t = fx—• 

TABLE No. 119 . 

Factors for Metal Tanks. 


Depth = h , 
in feet. 

Pressure = p, 
in lbs. 

Factor = /. 

fp 

S 

20 

8.68 

2.972 

.000573 

2 5 

10.85 

3- 22 3 

.000777 

3 ° 

13.02 

3-445 

.000996 

35 


3-643 

.001229 

40 

17-36 

3.824 

.001475 

5 ° 

21.70 

4.148 

.002000 

6o 

26.04 

4-43 2 

.002567 

8o 

34-72 

4.921 

.003797 

IOO 

43-40 

5*337 

.o° 5 i 47 

120 

52.08 

5 * 7 ° 2 

.006599 

140 

60.76 

6.031 

.008143 

160 

69.44 

6 - 33 1 

.009769 

180 

78.12 

6.608 

.011471 

200 

86.80 

6.867 

.013245 


The quotient of (fp)-i-s into the radius in inches gives 
the thickness of sheet, in inches, for the given depth, to 
resist pressure of toater only. 

561. Grades of Metals. —Pressure alone requires but 
very thin sheets of iron in the upper sections of small pipes, 
not enough to give the required rigidity. The upper sheets 
are liable to the most rapid deterioration by oxidations of 
any portion of the pipe, where they are subject to frequent 
alternate wettings and dryings by rises and falls of the 
water, and are most liable to strains by ice expansion, if 
the water surface is quiet during very cold weather. 

For such reasons the upper sheets should, in practice, 














LIMITING DEPTHS AND THICKNESSES OF METALS. 595 


be not less than three-sixteenths inch thick, with a stiffen¬ 
ing angle-bar at the top, and usually the top sheets are one- 
quarter inch thick. 

When the computed pressure strain calls for iron or 
steel sheets exceeding about one-quarter inch thickness, it 
is advisable for economy to use a good grade of metal, 
having ultimate tensile strengths of at least 40000 or 45000 
pounds per square inch. 

The upper sheets, where there is a large surplus of 
thickness, may be of a lower grade of iron, or 28000 to 
30000 pounds tensile resistance per square inch. 

562. Limiting Depths and Thicknesses of 
Metals. —Transposing the formula of thickness for varying 
pressures and diameters, 

f _ T v fP _ •4347^/ r 


we have the formula for depth, h , to which different thick¬ 
nesses of sheets for varying diameters of tanks, may extend, 
to sustain the internal pressure, with the given factor, 



ts 

.434/r x 12 


ts 

27604 ^/’ 



in which t — thickness of the metal sheet, in inches. 

s — ultimate cohesion of metal used, in lbs., per 
sq. in. 

d — diameter of tank, in feet. 
h depth from surface of water, in feet. 
f — factor of safety used, and found by interpola¬ 
tion in the above table, No. 119, of factors. 


Table No. 120, based on the above formula for 7^, will 
show at a glance the limiting depths below full water sur¬ 
face, at which given thicknesses of sheets must be changed in 





596 


TANK STAND-PIPES. 


C 

CM 


0 

£ 

W 

J 

CQ 

C 

h 



* 


The upper series of figured depths in this table refer to tanks exposed to wind forces. See § 564, p. 597. 









































THICKNESSES OF METALS. 597 



STAND-PIPE DIAGRAMS. 






































e os 


TANK STAND-PIPES. 


inclosed tanks, for various diameters of tanks, when their 
sheets vary in thickess by sixteenths of an inch. 

For instance, in the ten feet diameter tank the iron 
must not extend to more than 69 feet below full water sur¬ 
face ; iron to 85 feet depth ; T 5 g" iron to 100 feet depth ; 
and so on, by sixteenths, the f" iron not extending below 
167 feet depth. 

563. Thicknesses of Metals Graphically Shown. 

—The depths at which the thicknesses of metal sheets of 
inclosed stand-pipes may be most economically reduced 
from the base upward, using any assumed factor of safety, 
will be shown graphically, thus; plot the entire depth of 
water to scale in a vertical line, as an absciss, as in Figs. 
143 and 144, on a scale, say of ten feet to the inch ; plot 
the computed thickness of sheet at the base as a horizontal 

-JL. 

ordinate from the foot of the absciss ; draw this ordinate 
on a large scale, say 4 inches on a line equal 1 inch thick¬ 
ness of metal sheet; divide the portion of the ordinate 
representing one inch into sixteen equal parts ; connect the 
extreme of the ordinate with the top of the absciss with a 
straight inclined line if the same factor of safety is used 
for all depths of water; project vertical lines from each 
sixteenth division on the base ordinate, cutting the inclined 
line ; then the depths from the top by scale at which the 
sixteenth divisions cut the inclined line will be points of 
change, subject to standard widths of sheets that are 
graded in thickness by sixteenths of an inch. If a varying 
factor of safety for different depths is used, then the 
inclined line will be slightly curved to correspond with the 
equation of the factor. 

564. Exposed Stand-Pipes. —Considering the strains 
upon the metals near the bases of relatively tall uninclosed 
stand-pipes, by wind pressure leverages that tend to over- 


EXPOSED STAND-PIPES. 


599 


turn the structures, we find that a greater thickness of 
metal must be used at the base to resist this strain than to 
resist the bursting pressure of the water. 

We found (§ 556, p. 588) the leverage moment of the wind 

WH 

W ; = (.5PA) x .5H = 

£ 

and may safely assume a maximum pressure P of the wind 
as 40 pounds per square foot. 

Assuming that a relatively tali stand-pipe, if uninclosed, 
will lack both frictional and leverage stability unless an¬ 
chored to its foundation, and that the tank will be bolted 
to an ample weight of foundation to remain stable in 
position, then we may consider the empty tank as a vertical 
cantilever, and the leverage action of the wind TFi as tend¬ 
ing to rupture the shell at the base where its anchorage 
bolts take hold. 

The moment or resistance of the tank shell must at least 
equal the total wind pressure W into its leverage = 
W x MI 

In a vertical hollow cylindrical tank, secured at its base, 
the resistance of the metal at the base equals, very nearly, 
one-half the area of the horizontal section of metal into 
radius of the cylinder, into the tensile resistance per unit 
of section of metal. 

If the dimensions of metal are taken in inches, and W 
is the total pressure in pounds, then, for thickness at dis¬ 
tance H below top of tank, 

,5HW = (3.1416r^) x rs , (10) 


and 


WH 

1.5708rV 



Also if the dimensions are taken in feet and W and s in 
net tons, then, omitting factor of safety, 



600 


TANK STAND-PIPES. 


and 


18 . 8406 ^ 

H 

WH 

18.8406r 2 s ’ 


(12) 

(13) 


in which 


W = total pressure effect of wind, in tons. 
s = ultimate cohesion of metal, in tons, per 
sq. in. 

r — mean radius of tank shell, in feet. 

H — depth below top of tank, in feet. 
t x = thickness of metal shell, in inches, at depth 
H , that will just balance the wind leverage. 


Testing this formula for coefficients by four experiments 
by Sir Wm. Fairbairn, on thin hollow cylindrical beams 
supported at both ends and loaded in the middle, and 
taking W as equal 8 IF, we have in table No. 121 a mean 
coefficient equal .759. 


TABLE No. 121. 
Experiments with Hollow Cylindrical Beams. 


Breaking Load, 
pounds. 

Diameter. 

inches. 

Thickness. 

inches. 

Span. 

feet. 

Coefficient. 

2757 - 

12. 

•°37 

J 7 * 

•747 

ii6 37 - 

12.4 

• IJ 3 

15-625 

.888 

6 573 * 

17? 68 

.0631 

23-417 

.662 

14628. 

18.18 

.119 

23-417 

•739 




Mean .759 


Affixing to the last two formulas the coefficient c == .75 
and a factor f x equal 3.14, and we have for equation of 
thickness, 


W = 


18.840 §r 2 st x 



S.r 2 st x 

ir 


(tons). 



H 



















EXPOSED STAND-PIPES. 


601 


U 


H = 


WI I 

18.8406r 2 s x 
18.8406r 2 s^ 




(inches). (15) 
(feet). (16) 


r = Vssr (feet) - <”> 

It will be observed that this equation of t x to resist wind 

leverage is entirely different from the equation of t — T ^~ 

for static pressure of water. This, in tall pipes, increases 
as diameter decreases, while thickness for bursting pressure 
increases as diameter increases, so that if a series of each 
for similar conditions are plotted, their directions will be 
nearly at right angles. 

The greatest thickness given by either formula for given 
height and diameter will be used, or if computing for the 
depth to which a given thickness of sheet may be used in 
a given diameter of tank, then the least depth by either 
formula will be used in the exposed tank. 

The depths in tall stand-pipes at which the wind leverage 
resistance formula comes into use is indicated in Table 
No. 120, page 596, where two sets of figures are given for 
the same conditions, the upper figured depths being appli¬ 
cable to exposed stand-pipes, and the remaining figured 
depths being common for both inclosed and exposed stand¬ 
pipes. 

To the thicknesses thus determined from the table an 
addition should be made in the middle and lower portions 
of tall pipes to offset weaknesses from possible corrosions 
of the metal, so the factor of safety may be maintained for 
a long series of years. 

Frequent inspections and paintings are necessary for 
the long endurance of exposed tank stand-pipes, and 









602 


TANK STAND-PIPES. 


especial pains are to be taken to keep the cornice moldings, 
stiffening angles, exterior and interior ladder joints, and 
other details well protected with paint. 

565. Stand-Pipe Data. —A table of data relating to 
some of the tank stand-pipes constructed within a few 
years past has been inserted in the Appendix, and covers a 
large range of practice. 

Slender and tall stand-pipes are generally inclosed in a 
masonry tower. 

Most of the short tanks named of large diameter are 
mounted on masonry towers or iron trestles and are not 
inclosed. 

Many villages in the Middle States use tanks of wood 
with three or four inch staves hooped with iron. Such 
tanks are fifteen to thirty feet diameter, and twelve to 
twenty feet high, and are usually mounted on a wood 
trestle. 

* 

We have given illustrations of inclosed stand-pipes used 
at South Boston, Mass., Milwaukee, Wis., and Toledo, 
Ohio, and of exposed stand-pipes at South Abington, 
Mass., and Fremont, Ohio. 

In proportioning masonry towers for stand-pipes, the 
wind leverage action on the windward and resistance on 
the lee side, and the limiting pressures in the masonry are 
to be considered, also the limiting pressures in the founda¬ 
tions, as affected by weight carried and wind pressure 
leverage. 




















T 

j 

r 


s 


% 




e 


»_ 


sS 

t, 

5S 

3 , 















CHAPTER XX VI. 

SYSTEMS OF WATER SUPPLY. 


560. Permanence of Supply Essential.— Let the 

projector of a public water supply first make himself famil¬ 
iar with the possible scope and objects of a good and ample 
system of water supply, and become fully conscious of how 
intimately it is to be connected with the well-being of the 
people and their active industries in all departments of their 
arts, mechanics, trade, and commerce, as well as in their 
culinary operations, and let him also appreciate the conse¬ 
quences of its failure, or partial failure after a season of 
success. 

When the people have become accustomed to the ready 
flow from the faucets, at the sinks and basins, and in the 
shops and warehouses, then, if the pumps cease motion or 
the valve is closed at the reservoir, the household oper¬ 
ations, from laundry to nursery, are brought to a stand¬ 
still—engines in the shops cease motion, hydraulic hoists 
and motors in the warehouses cease to handle goods, rail¬ 
way trains, ocean steamers, and coasters delay for water, 
and a general paralysis checks the busy activity of the 
city. What a thrill is then given by an alarm of fire, be¬ 
cause there is no pressure or flow at the hydrants ! 

The precious waters of the reservoirs preside over cities 
with protecting influences, enhancing prosperity, comfort, 
safety and health, and are not myths, as were the goddesses 
in ancient mythology, presiding over harvests, flowers, 
fruits, health and happiness. 


604 


SYSTEMS OF WATER SUPPLY. 


Let the designer and builder of the public water system 
feel that his work must be complete, durable, and unfail¬ 
ing, and let this feeling guide his whole thought and 
energy, then there is little danger of his going astray as to 
system, whether it be called “ gravitation,” “ reservoir,” 
“stand-pipe,” or “direct pressure,” or of his being enam¬ 
ored with lauded but suspicious mechanical pumping au¬ 
tomatons, and uncertain valve and hydrant fixtures. 

When the people have learned to depend, or must of 
necessity depend, upon the public pipes for their indis¬ 
pensable water, it must flow unceasingly as does the blood 
in our veins. All elements of uncertainty must be over¬ 
come, and the safest and most reliable structures and ma¬ 
chines be provided. 

Many times, in different cities, a neglect, apparently 
slight, has cost, through failure, a fearful amount, when 
sacrificed life and treasure and a broad smouldering swarth 
across the city were the penalty. Having water-works is 
not always having full protection, unless they are fully 
adequate for the most trying hour. 

507. Methods of Gathering and Delivering Water. 
—There is no mystery about “ systems ” of water supply, 
as they have of late been often classified. The problem is 
simply to search out the best method of gathering or secur¬ 
ing an ample supply of wholesome water, and then to 
devise the best method of delivering that supply to the 
people. 

Usually there is one source whose merits and demerits, 
when intelligently examined, favorably outweighs the 
- merits and demerits of each and every other source, and 
there is usually one method of delivery that is conspicu¬ 
ously better than all others, when all the local exigencies 
are seen and foreseen. 


CHOICE OF WATER. 


605 


The usual methods of gathering the required supply are, 
to impound and store the rainfall or flow of streams among 
the hills ; draw from a natural lake ; draw from a running: 
river ; or draw from an artesian well. 

The usual methods of delivering water are, by gravita¬ 
tion from an elevated impounding basin ; elevation by 
steam or water power to a reservoir and from thence a flow 
by gravity; elevation to low and high service reservoirs, 
and from thence flow by gravity to respective districts ; and 
by forcing with pressure direct into the distribution-pipes, 
and cushioning the motion by a stand-pipe, or ample air- 
vessel and relief valve. 

568. Choice of Water. — The pumped supplies are 
usually drawn from lake, river, or subterranean sources. 

The selection of a lake or river water for domestic use is 
to be governed by considerations of wholesome purity ; and 
cautiousness of financial expenditure must not in this direc¬ 
tion exert too strong an influence in opposition to inflexible 
sanitary laws. 

This selection involves an intelligent examination of the 
origin and character of the impregnations and suspended 
impurities of the water, and the possibility of their thorough 
clarification. 

None of the waters of Nature are strictly pure. Some 
of the impurities are really beneficial, while others, which 
are often present, are not to be accepted or tolerated. A 
mere suspicion that a water supply is foul or unwholesome, 
even though not based on substantial fact, is often a serious 
financial disadvantage ; therefore earnest effort to maintain 
the purity of the water must extend also to the removal of 
causes of suspicion. 

Chemical science and microscopy are valuable aids in 
this portion of the investigation of the qualities of waters ; 


606 


SYSTEMS OF WATER SUPPLY. 


but we have detailed in the first part of this treatise so 
minutely the nature and source of the chief impurities, and 
so carefully pointed out those that are comparatively harm¬ 
less and those that are deadly, that an intelligent opinion 
can generally be readily formed ot the comparative puri¬ 
ties and values of different waters. We have also pointed 
out how waters may be clarified and conducted in their best 
condition to the point of delivery, and distributed in the 
most efficient manner. 

Predictions of any value as to quantity and quality of a 
supply from a proposed artesian well, demand a knowledge 
of the local geology and subterranean hydrology, which is 
rarely obtainable until the completion and test of the well; 
nevertheless we have shown the conditions under which a 
good supply of water may be anticipated with reasonable 
confidence. 

569. Gravitation. —When a good and abundant sup¬ 
ply of water can be gathered at a sufficient elevation, and 
within an accessible distance, the essential element of con¬ 
tinuous full-pressure delivery can then most certainly be 
secured, and in the matter of possible safety the gravitation 
method will usually be superior to all others. 

The quality of impounded water, when gathered in small 
storage reservoirs and from relatively limited watersheds, is 
subject to some of those unpleasant influences, heretofore 
referred to, which are to be provided against; and unless the 
hydrology and substructure of the gathering basin is well 
understood, the permanence of the supply may not fulfill 
enthusiastic anticipations. 

The value and importance of sufficient elevation of the 
supplying reservoir, when the delivery is by gravity, to 
meet the most pressing needs of the fire-service, ought not 
to be overlooked, for an efficient fire-service is usually one 


PUMPING WITH RESERVOIR RESERVE. 


607 


of the chief objects to be attained in a complete water 
supply. 

A water pressure of sixty to eighty pounds per square 
inch in the hydrants in the vicinity of an incipient fire, has 
a value which cannot be wholly replaced by a brigade of 
fire-steamers in commission, for with light-hose carriages 
and trained hosemen, connection will usually be made 
with the hydrants, streams be put in motion, and the fire 
overpowered before pressure is raised in the steamer’s boil¬ 
ers ; and the fire will not be suffered to assume unconquer¬ 
able headway during the delay. 

Constant liberal pressures in the hydrants is the first 
element of prompt and effective attack upon a fire immedi¬ 
ately after an alarm is given. Each moment lost before the 
beginning of an energetic attack increases greatly the diffi¬ 
culty of subduing the fire, and the probability of a vast 
conflagration. 

The element of distance of a gravitation supply, as re¬ 
gards cost of delivery, is an exacting one, and the lengths 
of conduit and large main are surprisingly short, while the 
balance of economy of delivery remains with the side of the 
gravitation scheme ; for conduits and mains are expensive 
constructions, and soon absorb more capital and interest 
than would pay for pumps and fuel for lifting a nearer 
supply ; still an element of safety is not to be sacrificed for 
a moderate difference in first cost. 

570. Pumping with Reservoir Reserve. — As re¬ 
gards safety and reliability of operation, w r e place second the 
method of delivery when the supply is elevated by hydrau¬ 
lic power, and third when it is elevated by steam power to 
a liberal-sized reservoir holding in store from six to ten 
days reserve of w r ater, from whence the supply flow T s by 
gravity into the distribution-pipes. If in such case there 


608 


SYSTEMS OF WATER SUPPLY. 


are duplicate first-class pumping-machines whose combined 
capacity is equal to the delivery of the whole daily supply 
in ten hours, or one-half equal to the delivery of the whole 
daily supply in twenty hours, then this method is scarcely 
inferior in safety to the gravitation method. 

The elements of safety may be equally secured in the 
low and high service method, when the physical features of 
the town or city make such division desirable. In a pre¬ 
vious chapter we have shown how a union of the high and 
low service may be made an especially valuable feature in 
efficient fire service. 

The records of nearly all the water departments of our 
largest cities, having duplicate pumping machinery, show 
how valuable and indispensable have been their reserve 
stores of water, and refer to the risks that would have been 
incurred had such reservoir storages been lacking. 

571. Pumping 1 with Direct Pressure. —We place 
fourth, as regards safety and reliability, the direct pressure 
delivery by hydraulic *power, and fifth, by steam power, 
with either stand-pipe or air-vessel cushions and safety 
relief-valves. 

The mechanical arrangements that admit of this method 
of delivery are simple, and several builders of pumping 
machinery have adapted their manufactures to its special 
requirements, but in point of continuous reliability the 
method still remains inferior to gravity flow. 

Even when the most substantial and most simple steam 
pumping machinery is adopted, if not supplemented by an 
elevated small reserve of water, this method of delivery is 
accompanied with risks of hot bearings, sudden strains, 
unexpected fracture of connection, shaft, cylinder, valve- 
chest or pipe, and occasional necessary stoppages. 

The best pumping combinations are so certainly liable 



PUMPING WITH DIRECT PRESSURE. 


609 


to such contingencies that cities may judiciously hesitate to 
rely entirely upon the infallibility of then boilers, engines, 
and pumps, even when so fortunate as to secure attendants 
upon whom they can place implicit confidence. 

The direct pressure method, alone, necessitates unceas¬ 
ing firing of the boiler and motion of the pumping-engine, 
and consequently double or triple sets of hands, to whose 
integrity and faithfulness, night and day and at all times, 
the works are committed. 

Hydraulic power and machinery are far more reliable 
than steam machinery, for direct pressure uses, and hy¬ 
draulic power presents the great advantage of being able 
to respond almost instantaneously to the extreme demand 
for both water and pressure, while a dull fire under the 
boiler may require many minutes for revival so as to raise 
the steam to the effective emergency pressure. An example 
of pumping machinery of five million gallons capacity per 
diem, driven by hydraulic power, is shown in Fig. 143. 
This set of pumping machinery was constructed for the city 
of Manchester, N. H., by the G-eyelin department of Messrs. 
R. D. Wood & Co., Philadelphia, from general designs by 
the writer, and has operated very satisfactorily since its 
completion in 1874. This machinery is adapted in all re¬ 
spects to direct pressure service, and was so used during a 
full season while the reservoir was in process of construction, 
and it is equally well adapted to its ordinary work of pump¬ 
ing water to the distributing reservoir. 

The direct forcing method does not provide for the de¬ 
position or removal of impurities after they have passed the 
engine, but the sediments that reach the pumps are passed 
forward to the consumers in all sections of the pipe distri¬ 
bution. 

In combination with a reservoir sufficient for all the 


610 


SYSTEMS OF WATER SUPPLY. 


ordinary purposes, and equalizing the ordinary work and 
the ordinary pressures at the taps, and also in combination 
with a very small reservoir, the direct pressure facilities 
may prove a most valuable auxiliary in times of emergency, 
and they are then well worth the insignificant difference in 
first cost of pumping machinery. 

In the smaller works the entire machinery, and in larger 
works one-half the machinery, may with advantage be 
capable of and adapted for direct pressure action. 

If, instead of substantial and simple machinery built 
especially for long and reliable service, some one of the 
intricate and fragile machines freely offered in the market 
for direct pumping is substituted, and is not supplemented 
by an ample reservoir reserve, then a risk is assumed which 
no city can knowingly afford to suffer; and if true prin¬ 
ciples of economy of working are applied, it will generally 
be found that no city can, upon well-established business 
theories, afford to purchase and operate such machinery. 

Well designed and substantially constructed pumping- 
machines, such as are now offered by several reliable build¬ 
ers, when contrasted with several of the low-priced and low- 
duty contrivances, are most economical in operation, most 
economical in maintenance, and infinitely superior in reli¬ 
ability for long-continuous work. 


APPENDIX. 

THE METRIC SYSTEM OF WEIGHTS AND MEASURES. 

Tlie use of the metric system of measure and weights 
was legalized in the United States in 1866 by the National 
Government, and is used in the coast survey by the engineer 
corps, and to considerable extent in the arts and trades. 

Several of the best treatises on theoretical hydraulics 
give their lengths and volumes in metric measures, and we 
give their equivalents in United States measures in the 
following tables. 

The metre , which is the unit of length , arm, and volume, 
equals 39.87079 inches or 3.280899 feet in length lineal, and 
along each edge of its cube. 

This unit is, for measures of length, multiplied decimally 
into the decametre , hectometre , kilometre , and myriametre , 
and is subdivided decimally into the decimetre , centimetre , 
and millimetre. 

The affixes are derived from the Greek for multiplication 
by ten, and from the Latin for division by ten. 

The measures for surface and volume are similarly 
divided. 

The gramme is the unit of weight, and it is equal to the 
weight of a cubic centimetre of water, at its maximum 
density, in vacuo. = .0022046 lbs. 

A cubic metre of water, at its maximum density, weighs 
2204.6 lbs. avoir. 

38 


612 


APPENDIX. 


Table of French Measures and United States Equivalents. 


Measures of Length. 



No. of 
Metres. 


i Millimetre . 

.OOI 

= *0393708 inch = .0032809 foot. 

— -3937°8 inch = .032809 foot. 

— 3.93708 inches = .3280899 ft. = .1093633 yd. 

— 39-37o8 inches =: 3.2808992 ft. = .198842 rod 

i Centimetre . 

i Decimetre . 

.01 

. 1 

i Metre . 

1 i 

i Decametre . 

( 

IO 

= .0006214 mile. 

= 32.808992 ft. = 1.98842 rods = .0062138 mile. 
= 328.08992 ft. = 19.88424 rods = .062138 mile. 
= 3280.8992 ft. = 198.8424 rods = .621383 mile. 
== 32808.992 ft. = 1988.424 rods = 6.21383 miles. 

i Hectometre . 

i Kilometre . 

i Myriametre . 

IOO 

IOOO 

10000 


Measures of Area. 



No. of sq. 
Metres. 


1 Centiare. 

H 

IO 

IOO 

IOOO 

IOOOO 

= 10.7643 sq. ft. = 1.196033 sq. yds. == .039538 
sq. rod. 

= 107.643 sq. ft. = .39538 sq. rd. = .002471 acre. 
= 1076.43 sq. ft. = 3.95383 sq. rds. = .02471 acre. 
= 10764.3 sq.ft. = 39.5383 sq. rds. = .2471 acre. 
= 107643 sq. ft. = 395.383 sq. rds. = 2.471 acres. 

1 Deciare. 

1 Are. 

1 Decare (not used) 
1 Hectare. 



Measures of Volume. 



No. of cu. 
Metres. 


1 Millilitre. 

.000001 

.OOOOI 

.OOOl 

.OOI K 

.01 j 
.1 j 

I •] 

= .0610279 cubic inch. 

= .610279 cubic inch. 

= 6.10279 cu. i ns - = -o°353 cu. ft. = .0264165 gal. 

= 61.0279 cu - ins. = .0353136 cu. ft. = .264165 
gallon. 

= 610.279 cu - i ns - = • 353 i 36 cu. ft. = .0130791 
cu. yard. 

= 26.4165 gallons = 3.53136 cu. ft. = .130791 cu. 
yard. 

= 264.1651 gallons = 35.313 cu. ft. = 1.30791 
cubic yards. 

1 Centilitre. 

1 Decilitre. 

1 Litre. 

1 Decalitre. 

1 Hectolitre. 

1 Kilolitre. 













































APPENDIX. 


613 


Table of French Measures and United States Equivalents 

(Continued ). 

Measures of Solidity. 


• 

No. of cu. 
Metres. 


i Millistere. 

.OOI 

.OI \ 

• x ! 

1 1 
IO 

IOO 

IOOO 

= 61.0279 cubic inches = .03532 cubic foot. 

= 610.279 cu. ins. = .353166 cu. ft. = .013079 cu. 
yard. 

6102.79 cu - ins. = 3.53166 cu. ft. = .130791 cubic 
yard. 

= 61027.9 cu. ins. = 35.3166 cu. ft. = 1.30791 cu. 
yards. 

= 353.166 cu. ft. = 13.0791 cu. yards. 

= 3531.66 cu. ft. =■ 130.791 cu. yards. 

= 35316.6 cu. ft. = 1307.91 cu. yards. 

1 Centistere. 

1 Decistere. 

1 Stere. 

1 Decastere. 

1 Hectostere. 

1 Kilostere. . . 



Measures of Weight. 



No. of 
Grammes. 


1 Milligramme .... 

• OOI 

= .015432 grain. 

1 Centigramme. ... 

• OI 

= .15432 grain. 

1 Decigramme. 

. I 

= 1.5432 grains = .0035274 oz. Avoir. 

1 Gramme. 

I 

= 15.432 grs. = .035274 oz. Av. = 002205 lb. Av. 

1 Decagramme. 

IO 

= 154.32 grs. = .35274 oz. Av. = .02205 lb. Av. 

1 Hectogramme .. . 

IOO 

= 1543.2 grs. = 3.5274 oz. Av. = .2205 lb Av. 

1 Kilogramme. 

IOOO 

= 15432 grs. = 35.274 oz. Av. = 2.205 lbs. Av. 

1 Tonne. 

• • • • 

= 2204.737 lbs. 


A cubic incli is equal to 

.004329 gallon; or .0005787 cu. ft; or 16.38901 millilitres; or 1.638901 
centilitres; or .1638901 decilitre; or .016389 litre; or .016389 millistere ; or 
•0016389 centistere. 

A gallon is equal to 

231 cubic inches, .13368 cubic foot; or .031746 liquid barrel; or 3785.513 
millilitres ; or 378.551 centilitres ; or 37.8551 decilitres ; or 3-785513 litres ; or 
.3785513 decalitre ; or .037855 hectolitre ; or .0037855 kilolitre. 

A cubic foot is equal to 

1728 cubic inches; or 7.48052 liquid gallons; or 6.2321 imperial gallons; 
or 3.21426 U. S. pecks ; or .803564 U. S. struck bushel; or .23748 liquid bar- 






























614 


APPENDIX. 


rel of 31*- gallons; or 2831.77 centilitres; or 283.177 decilitres: or 28.3177 
litres ; or 2.83177 decalitres ; or .283177 hectolitre ; or .0283177 kilolitre ; or 
28.3177 millisteres; or 2.83177 centisteres ; or .283177 decistere ; or .0283177 
stere. 

The imperial gallon is equal to 

.16046 cu. feet ; or 1.20032 U. S. liquid gallons. 

A cubic yard is equal to 

46656 cu. inches ; or 201.97404 liquid gallons ; or 27 cu. feet ; or 21.60623 
struck bushels ; or 764.578 litres ; or 76.4578 decalitres ; or 7.64578 hectolitres ; 
or .764578 kilolitre ; or 764.578 milisteres ; or 76.4578 centisteres ; or 7.64578 
decisteres ; or .764578 stere; or .0764578 decastere ; or .0076458 hectostere; 
or .00076458 kilostere. 


Table of Units of Heads and Pressures of Water and 

Equivalents. 


(Rankine.) 


One foot of water at 52°.3 Fah. 


< i 
ii 


U 

u 


u 

u 


u 

u 


One lb, on the square foot 
“ “ “ inch 

One atmosphere (— 29.922 in. mercury) 
One inch of mercury, at 32 0 
One cubic foot of average sea-water 


62.4 

•433 

.0295 

.8823 

.016026 

2.308 

33-9 

I-I 334 

1.026 


lbs. on the square foot. 

inch. 

atmosphere. 

inch of mercury at 32 0 . 

foot of water. 

feet of water. 

U U 

U i( 

cu. ft. of pure water in 
weight. 


One Fahrenheit degree 

One Centigrade degree 

Temperature of melting ice 
« << 


= -55555 Centigrade degree. 

= 1.8 Fahrenheit degrees. 

= 32 0 on Fahrenheit’s scale. 

= 0 “ Centigrade scale. 



APPENDIX. 


615 


Table of Average Weights, Strengths, and Elasticities of 
Materials.— (From Trautwine, Neville, and Rankine.) 


Materials. 


Weight 
per 
cu. in. 


Weight Specific 
per Grav. 
cu. ft. 


Woods (seasoned, and dry). 


Lbs. 


Ash... 

“ American white.... 

Beech. 

Cedar, American. 

“ “ green 

Chestnut.. 

Elm. 

“ very dry. 

Hemlock. 

Hickory. 

Maple. 

Oak, live. 

“ white. 

“ red. 

Pine, white. 

“ northern yellow 
“ southern 

Spruce . 

Walnut, black. 


Lbs. 

48.0 

33 

48 

47 

56.8 
4i 

36.8 
35 

25 

53 

49 
59-3 
51-8 
40.0 
25.0 
34-3 
45-0 
25.0 
38 


77 

61 

77 

75 

9i 

66 

59 


56 

40 

85 


79 

95 

33 

40 

55 

72 

40 

61 


Metals. 


Aluminum. 

Brass, cast. 

rolled. 

“ wire. 

Bronze (copper 8 parts, tin 1 part).... 

Copper, cast. 

“ sheet.. 

“ wire, drawn. 

Glass. 

Iron, cast, cold blast. 

“ “ hot blast. 

“ “ wrought, sheet or plate.... 

“ “ “ large bars. 

Lead, cast. 

“ milled.. 

Mercury (at 32 Fah., 849 lbs.) (at 212 

836lbs.), at 60 J .°. 

Silver. 

Steel. 

Tin, cast. 

Zinc. 


0972 162 

3038525 

... :524 

3085 533 
3062 529 
3 ii 3 538 
••• 549 
3241 560 

0885] 153 
2552 444 


... 1443 
2807 485 


.... 474 
. .4152 717 

.... 713 

.. 4896 846 


373 

2836 

2637 

2532 


644 

490 

456 

437 


Earth and Stones (dry). 

Asphaltum. 

Brick, common hard. 

“ soft inferior. 

“ best pressed. 

Cement, American Rosendale, loose. ... 
“ “ Louisville. 


Cu. ft. 

87-3 

125 

100 

150 

56 

49.6 


Cu. yd. 

2357 

3375 

2700 

4050 

1512 

1339 


2.6 
8.40 
8.40 
8.54 
8-5 
8.61 
8.80 
8.88 
2-45 
7 -11 
7.04 

7-77 

7.60 

11.44 

11.40 

I3-58 

10.31 

7.85 

7-30 

7.00 


1.4 


Tenacity 
per 
sq. in. 

Resist¬ 
ance per 
sq. in. to 
crush¬ 
ing force. 

Lbs. 

Lbs. 

17000 

9000 

16000 

8500 

• • • • 

4900 

11400 

5600 

12000 

• • • • 

13500 

10300 

• • • • 

• • • • 

• • • • 

• • • • 

I 3 COO 

6400 

16000 

6500 

10250 

• • • • 

6000 

• • • • 

7800 

• • • • 

5400 

12400 

5500 

• • • • 

7200 

• • • • 

l8000 

• • • • 

10300 

49OOO 


36000 


I9OOO 


30000 


60000 


9400 

33000 

I67OO 

106000 

13500 

10S000 

50000 


480OO 


l800 


3300 


4O9OO 


120000 


5300 


7500 


• • • • 

280 

• • • • 

• • * » 

800 

• • • • 

• • • • 

• • • • 

• • • • 

• • • t 
















































































616 


APPENDIX. 


Table of Average Weights, Strengths, Etc.—( Continued ). 


Materials. 

Weight 
per 
cu. ft. 

1 

Weight 
per 
cu. yd. 

Specific 

Grav. 

Tenacity 
per 
sq. in. 

Resist¬ 
ance per 
sq. in. to 
crush¬ 
ing force. 


Lbs. 

Lbs. 


Lbs. 

Lbs. 

Cement, English Portland. 

90 

2430 


280 

• • • • 

French Boulogne. 

80 

2160 



• • • • 

Clay, potter’s. 

II 9 

3213 

1.9 


.... 

“ dry, in lump, loose. 

63 

1701 




Concrete. 

. . 

• • • • 



556 

Coal, bituminous. 

84 

2268 

i -35 



“ broken, loose. 

50 

1350 



• • • • 

“ a ton occupies 43 to 48 cu. ft. 

• • • • 

• • • • 



• • • • 

Earth, loam, loose. 

75 

2025 




“ “ moderately rammed. 

95 

2565 



• • • • 

as a mud. 

no 

2970 




Granite. 

168 

4536 

2.69 


IOOOO 

“ quarried, in loose piles. 

96 

2592 



* • • • 

Gneiss. . 

168 

4536 

2.69 


• • • • 

“ quarried, in loose piles. 

100 

2700 



• • • • 

Greenstone. 

187 

5049 




“ auarried, in loose piles. 

107 

2889 



• • • • 

Gravel. 

100 

2700 



• • • • 

“ moderately rammed, dry. 

120 

3240' 

1.90 


• • • • 

“ “ moist. 

130 

3510 



• • • • 

Limestone. 

168 

4536 

2.7 


8333 

Lime, ground, loose. . 

53 

1431 




Marble. 

165 

4455 

2.64 


5500 

Masonry, dressed granite, or limestone.. 

165 

4455 




“ well-scabbled mortar rubble of do. 

154 

4158 




“ “ “ dry “ “ do. 

138 

3726 



• • • • 

“ roughly “ “ “ “ do. 

125 

3375 



• • • • 

“ dressed sandstone. 

144 

3888 




“ dry rubble “ .. 

no 

2970 




“ brickwork, medium. 

125 

3375 



345 

“ “ coarse. 

100 

2700 




“ “ press’d bricks, close joints 

140 

3780 



• • • • 

Marl. 

no 

2970 

i -75 


.... 

Mortar, cement. 

103 

2781 

1.65 

50 


Peat, unpressed. 

25 

675 

• • • • 



Sand,loose. 

100 

2700 

• • • • 



“ shaken. 

no 

2970 

1.76 


• • • • 

“ wet. 

125 

3375 

• • • • 



Sandstone. 

150 

4050 

* • • • 


5000 

quarried, in loose pile. 

86 

2322 

• • • • 


• • • • 

Slate . 

180 

4873 

2.89 


12000 

Soapstone, or steatite. 

170 

459 ° 

2-73 


• • • • 

Miscellaneous Materials. 







58.7 

1585 

0.94 

• • • • 

200 

Leather. 


• • • • 

• • • • 

4200 


Oil, linseed. 

58.68 

• • • • 

•94 



Petroleum. 

54.81 

• • • • 

.878 



Powder, slightly shaken. 

62.3 

• • • • 

1.0 



Snow, loose. 

12 

324 

.... 



“ wet and compact. 

50 

1350 

• • • • 



Water. 

62.334 

1693 

1.0 



























































































APPENDIX. 


617 


Formulas for Shafts.— (Francis.) 
Wrouglit-iron prime movers, with gears: 

d = and P .OliVS 3 . 

Wrought-iron transmitting shaft: 




and P = .02 IVd 3 . 


Steel prime mover, with gears: 


d = an ,i p - .016ira». 

N 


Steel transmitting shaft: 


d = rf ‘ S1 f P , and P = .032 JSfd 3 . 


In which d = diameter of shaft in inches. 

N = number of revolutions per minute. 
P = horse powers. 


Trigonometrical Expressions. 


COTANGENT 




Radius = AC. 
Sine = Cd. 

Cosine = Ce. 
Tangent = Bf. 
Cotangent = lig. 
Secant = Af. 
Cosecant = Ag. 
Versine = Bd. 
Coversine = lie. 














618 


APPENDIX. 


« 

Trigonometrical Equivalents, when Radius = i. 


Sine = 

1 -f- Cosec. 

u _ 

Cosin. -i- Cotan. 

a _ 

V(1 — Cosin 2 .) 

Cosine = 

1 -r- Sec. 

U — 

Sin. -r- Tan. 

a __ 

Sin. x Cotan. 

u _ 

Vl — Sin 2 . 

Tangent = 

1 -r- Cotan. 

u _ 

Sin. -f- Cosin. 

Cotangent = 

1 -T- Tan. 

cc _ 

Co sin. -f- Sin. 

Secant = 

1 -T- Cosin. 

u _ 

Vl + Tan 2 . 

Cosecant = 

1 -r- Sin. 

<< _ 

Vl + Cotail 2 .' 

Versine = 

Rad. — Cosin. 

Coversine = 

Rad. — Sin. 

Complement = 

90° — Angle. 

Supplement = 

180° — Angle. 

If radius of an arc of any angle is multiplied or divided 

by any given number, then its several correspondent trigo- 

nometrical functions are 

increased or diminished in like 

ratio. 


Diameter 

= Rad. x 2. 

Circumference 

= Rad. x 6.2832. 

u 

= Diam. x 3.1416. 

Area of circle 

= Diam 2 . x .7854. 


Surface of a sphere = Diam 2 . x 3.1416. 
Volume of a sphere = Diam 3 . x .5236. 


Length of one second of arc = Rad. x .0000048. 
“ “ “ minute “ “ = Rad. x .0002909. 

“ “ “ degree “ “ = Rad. x .0174533. 


« a 






APPENDIX. 


619 


Values* of Sines, Tangents, Etc., when Radius = 


Deg. 

Sine. 

Cover. 

Cosec. 

Tang’t. 

Cotan. 

Secant. 

Versine. 

Cosine. 

De g. 

O 

.OO 

I.OOOOO 

Infinite. 

.O 

Infinite. 

I.OOOOO 

0. 

I.OOOOO 

90 

I 

.oi745 

.98254 

57.2986 

•01745 

57.2899 

1.00015 

.OOOI 

.99984 

89 

2 

.03480 

.96510 

28.6537 

.03492 

28.6362 

1.00060 

.0006 

•99939 

88 

3 

•05234 

•94766 

19.1073 

.05241 

19.0811 

1-00137 

.0013 

.99863 

87 

4 

.06976 

.93024 

14-3355 

.06993 

14.3007 

1.00244 

.0024 

•99756 

86 

5 

.08716 

.91284 

11-4737 

.08749 

11.4300 

1.00381 

.0038 

.99619 

85 

6 

.10453 

•89547 

9.5667 

.10510 

9-5144 

I 00550 

.0054 

.99452 

84 

7 

.12187 

.878x3 

8.2055 

.12278 

8.1443 

1.00750 

.0074 

•99255 

83 

8 

•13917 

.86 o 32 

7.1852 

•14054 

7-1154 

1.00982 

.0097 

.99027 

82 

9 

•15643 

.84356 

6.3924 

.15838 

6.3137 

1.01246 

.0123 

.98769 

81 

IO 

•17365 

.82035 

5-7587 

.17633 

5-6712 

1.01542 

.0151 

.98481 

80 

II 

.19081 

.80919 

5.2408 

•19438 

5.1446 

1.01871 

.0183 

.98163 

79 

12 

.2O79I 

.79208 

4.8097 

•21255 

4.7046 

1.02234 

.0218 

•97815 

78 

13 

.22495 

•77504 

4-4454 

.23087 

4-3315 

1.02630 

.0256 

•97437 

77 

14 

.24I92 

•75807 

4-1335 

•24933 

4.0108 

1.03061 

.0297 

.97030 

76 

15 

.25882 

.74118 

3- 8 637 

•26795 

3.7320 

1.03527 

.0340 

•96593 

75 

l6 

•27564 

.72436 

3-6 i 79 

.28674 

3-4874 

1.04029 

.0387 

.96126 

74 

*7 

.29237 

.70762 

3-4203 

•30573 

3.2708 

1.04569 

.0436 

•95630 

73 

18 

.30902 

.69098 

3.2360 

•32492 

3-0777 

1.05146 

.0489 

.95106 

72 

19 

•32557 

•67443 

3-07I5 

•34433 

2.9O42 

1.05762 

•0544 

•94552 

/i 

20 

.34202 

•65797 

2.9238 

•36397 

2-7475 

1.064x7 

.0603 

•93969 

70 

21 

•35837 

.64163 

2.7904 

.38386 

2.6051 

1.07114 

.0664 

•93358 

69 

22 

•37461 

.62539 

2.6694 

.40403 

2.4751 

1.07853 

.0728 

.92718 

68 

23 

•39073 

.60926 

2 5593 

•42447 

2-3558 

X.08636 

.0794 

.92050 

67 

24 

.40674 

•59326 

2-4585 

•44523 

2.2460 

1.09463 

.0864 

•91355 

66 

25 

.42262 

•57738 

2.3662 

.46631 

2.1445 

I.10337 

.0936 

.90630 

65 

26 

.43837 

.56162 

2.2811 

•48773 

2.0503 

1.11260 

.1012 

.89879 

64 

27 

•45399 

.54600 

2.2026 

•50952 

1.9626 

1.12232 

.1089 

.89101 

63 

28 

.46947 

.53 0 52 

2.1300 

•53171 

1.8807 

1.13257 

.1170 

.88295 

62 

29 

.48481 

•51519 

2.0626 

.55431 

1.8040 

1-14335 

•1253 

.87462 

61 

30 

.50000 

.50000 

2.0000 

•57735 

1.7320 

1.15470 

•1339 

.86603 

60 

31 

•51504 

.48496 

1.9416 

.60086 

1.6643 

1.16663 

.1428 

•85717 

59 

3 2 

.52992 

.47008 

1.8870 

.62487 

1.6003 

I-I79I7 

.1519 

.84805 

58 

33 

•54464 

•45536 

1.8360 

.64941 

I-539 8 

1.19236 

•1613 

.83867 

57 

34 

.55919 

.44080 

1.7882 

•67451 

1.4826 

1.20621 

.1709 

.82904 

56 

35 

•57358 

.42642 

1-7434 

.70020 

1.4281 

1.22077 

.1808 

.81915 

55 

3 6 

•58778 

.4x221 

1-7013 

.72654 

1-3764 

1.23606 

.1909 

.80902 

54 

37 

.60181 

•39818 

1.6616 

•75355 

1.3270 

1.25213 

.2013 

.79864 

53 

38 

.61566 

•38433 

1.6242 

.78128 

1.2799 

1.26901 

.2110 

.78801 

52 

39 

.62932 

.37067 

1.5890 

.80978 

1-2349 

1.28675 

.2228 

•77715 

51 

40 

.64279 

•35721 

1-5557 

.83970 

1.1918 

1.30540 

•2339 

.76604 

50 

41 

.65606 

•34394 

1.5242 

.86929 

1.1504 

1.32501 

.2452 

•75471 

49 

42 

.66913 

.33086 

1.4944 

.90040 

1.1106 

1.34563 

.2568 

•74314 

48 

43 

.68200 

.31800 

1.4662 

•93251 

1.0724 

1.36732 

.2686 

•73135 

47 

44 

.69465 

•30534 

1-4395 

96569 

1 0355 

1.39016 

.2808 

•71934 

46 

45 

.70711 

.29289 

I.4I42 

1. 

I. 

1.4x421 

.2928 

.70711 

45 


Cosine. 

Versine. 

Secant. 

Cotan. 

Tang’t. 

Cosec. 

Cover. 

Sine. 



* When the angle exceeds 45 0 , read upward ; the number of degrees will then be found in 
the right-hand column, and the names of columns at the bottom. 






















































620 


APPENDIX. 


In Right-Angled Triangles. 

Base = PHyp a . — Perp 2 . 

“ = P(Hyp. + Perp.) x (Hyp. — Perp.) 

Perpendicular = PHyp. 2 — Base 2 . 

“ = P(Hyp. + Base) x (Hyp. — Base.) 

Hypotlienuse = PBase 2 + Perp 2 . 


What constitutes a car load (20,000 lbs. weight ): 

70 bbls. lime; 70 bbls. cement; 90 bbls. flour; 6 cords 
of hard wood ; 7 cords of soft wood ; 18 to 20 head of cattle ; 
9000 feet board measure of plank or joists; 17,000 feet 
siding ; 13,000 feet of flooring ; 40,000 shingles ; 340 bushels 
of wheat; 360 bushels of corn; 680 bushels of oats; 360 
bushels of Irish potatoes; 121 cu. ft. of granite ; 133 cu. ft. 
sandstone; 6000 bricks; 6 perch rubble stone ; 10 tons of 
coal; 10 tons of cast-iron pipes or special castings. 

Lubricator , for slushing lieary years: 

10 gallons, or 3J pails of tallow; 1 gallon, or J pail of 
Neat’s foot-oil; 1 quart of black-lead. Melt the tallow, 
and as it cools, stir in the other ingredients. 

For cleaning brass: 

Use a mixture of one ounce of muriatic acid and one- 
lialf pint of water. Clean with a brush ; dry with a piece 
of linen ; and polish with fine wash leather and prepared 
hartshorn. 

Iron cement , for repairing cracks in castings: 

Mix l lb. of flour of sulphur and J lb. of powdered sal 
ammoniac with 25 lbs. of clean dry and fine iron-borings, 
then moisten to a paste with water and mix thoroughly. 










APPENDIX. 


621 


Calk the cement into the joint from Ibotli sides nntil the 
crack is entirely tilled. In heavy castings to be subjected 
to a great pressure of water, a groove may be cut along a 
transverse crack, on the side next the pressure, about one- 
quarter inch deep, with a chisel ^-inch wide, to facilitate 
the calking in of the cement. 

Alloys .—The chemical equivalents of copper, tin, zinc, 
and lead bear to each other the following proportions, ac¬ 
cording to liankine: 

Copper. Tin. Zinc. Lead. 

3 x -5 59- 3 2 -5 103.5 

When these metals are united in alloys their atomic pro¬ 
portions should be maintained in multiples of their respec¬ 
tive proportional numbers ; otherwise the mixture will lack 
uniformity and appear mottled in the fracture, and its 
irregular masses will differ in expansibility and elasticity, 
and tend to disintegration under the influence of heat and 
motion. 


Materials. 


Composition. 


By Equivalents. 

By Weight. 

Very hard bronze. 

Copper. 

12 

Tin. 

I 

Copper. 

6.401 

Tin. 

I 

Hard bronze, for machinery bearings. 

14 

I 

6.966 

I 

Bronze or gummetal, contracts in cooling 

16 

I 

8.542 

I 

Bronze, somewhat softer. 

18 

I 

9.610 

I 

Soft bronze, for toothed wheels. 

20 

I 

IO.678 

I 

Malleable brass. 

Copper. 

4 

Zinc. 

I 

Copper. 

3-877 

Zinc. 

I 

Ordinary brass, contracts g 1 ^ in cooling. 

2 

I 

1.938 

I 

Yellow metal, for sheathing ships. 

3 

2 

1-454 

I 

Spelter solder, for brazing copper and iron.. 

4 

3 

1.292 

I 


Babbitt’s metal consists of 50 parts of tin, 1 of copper, and 5 of antimony. 





















622 


APPENDIX. 


Aluminum bronze, containing 95 to 90 parts of copper 
and 5 to 10 parts of aluminum, is an alloy much stronger 
than common bronze, and has a tenacity of about 22.6 
tons per square inch, while the tenacity of common bronze, 
or gun-metal, is but about 16 tons. 

Manganese bronze is made by incorporating a small 
proportion of manganese with common bronze. This alloy 
can be cast, and also can be forged at a red-heat. 

A- specimen cast at the Royal Gun Factory, AYoolwicli, 
’in 1876, showed an ultimate strength of 24.3 tons per square 
inch, an elastic limit of 14 tons, and an elongation of 8.75 
per cent. The same quality forged had an ultimate resist¬ 
ance of 29 tons per square inch, an elastic limit of 12 tons, 
and an elongation of 31.8 per cent. A still harder forged 
specimen had an ultimate strength of 30.3 tons per square 
inch, elastic limit of 12 tons, and elongation of 20.75 per 
cent. 

The tough alloy, introduced by Mr. M. P. Parsons, will 
prove a desirable substitute for the common bronze in hy¬ 
draulic apparatus, where its superior strength and greater 
reliability will be especially valuable. 


Approximate Bottom A elocities of flow in Channels at 

* WHICH THE FOLLOWING MATERIALS BEGIN TO MOVE. 

2.5 feet per second, microscopic sand and clay. 

•5° “ “ “ fine sand. 

coarse sand, 
pea gravel. 


1.00 


i-75 

3 

4 

5 


(C 

« a 

<( u 


C( (( 

(t a 

« a 


a 

« 

u 

(i 

(( 

(C 


smooth nut gravel. 

1 pinch pebbles. 

2-inch square brick-bats. 


APPENDIX 


623 


Tensile Strength of Cements and Cement Mortars, when 
7 Days old, 6 of which the Cements were in Water. 

(Compiled from Gillmore.*) 


How Mixed. 

By Weight. 

By Volume, 
Loosely Measur’d 

By Volume, 

WELL SHAKEN. 



c n 
£ 

O 

w 

.a 

to 

*3 

£ 

§ 
tJ s 

O <0 

a<o 

Rosendale Cement. 

- 1 

Sand. 

1 

[ Weight per U. S. bu., 
loosely measured, 

[ 120 lbs. 

Rosendale { W , ei S ht P er U * s - bu -, 
Cement j measured, 

Sand. 

Portland Cement. 

Rosendale Cement. 

Sand. 

Tensile strength per square inch. 

d vpM 

.S .£ .S 

m in 0 

to in co 

c n 

0 

O 

Portland 
Cement ( 

Crushing ) 

wt. per | 

sq. in. ) 









• 



Lbs. 

Lbs. 

Like beton agglomere. 

1 

— 

•25 

X 

— 

.21 

I 

— 

•25 

377 

— 

44 

common mortar.. 

1 

— 

•25 


— 



— 


289 

— 

44 

beton agglomere. 

1 

— 

•5 

I 

— 

.42 

I 

— 

•5 

320 

— 

u 

common mortar.. 

I 

— 

•5 


— 



— 


222 

— 

14 

beton agglomere. 

I 

— 

X 

I 

— 

.85 

I 

— 

•99 

244 

— 

4 C 

common mortar.. 

I 

— 

1 


— 



— 


197 

— 

44 

beton agglomere. 

I 

— 

i -33 

1 

— 


I 

— 

r -3 

179 

— 

44 

common mortar.. 

I 

— 

I -33 


— 



— 


129 

— 

44 

beton agglomere. 

I 

— 

2 

I 

— 

l [7 

I 

— 

1.9 

138 

2804.4 

44 

common mortar.. 

I 

— 

2 

44 

— 



— 


IO9 

1038.0 

44 

beton agglomere. 

I 

— 

6 

I 

— 

5 

1 

— 

5-9 

66 

259-5 

44 

common mortar.. 

I 

— 

6 


— 



— 


35 

— 

44 

beton agglomere. 

I 

— 

8 

I 

— 

6.8 

I 

— 

7.8 

39 

259-5 

44 

common mortar.. 

I 

— 

8 


— 



— 


24 

104.7 

44 

beton agglomere. 

I 

8 

— 

1 

— 

11.6 

— 

— 

— 

96 

— 

44 

common mortar.. 

I 

8 

— 


— 


— 

— 

— 

40 


44 

beton agglomere. 

I 

2 

— 

I 

— 

2 l? 

— 

— 

— 

129 

— 

44 

common mortar.. 

1 

2 

— 

44 

— 


— 

' 

— 

44 

— 

44 

beton agglomere. 

— 

I 

I 

— 

— 

— 

— 

— 

— 

5 1 

— 

44 

44 U 

— 

I 

2 

—■ 

I 

1.2 

— 

I 

1.4 

40 

310.7 

44 

44 44 

— 

I 

3 

— 

I 

1.8 

— 

I 

2 

33 

116.4 

44 

44 44 

- 

I 

4 

— 

1 

2.4 

— 

I 

2.8 

22 

156.0 











( 

Less than 


44 

44 44 

— 

1 

6 

— 

X 

3-6 

“““ 

1 

4 1 

10 lbs. 

52.4 

44 

44 44 

— _ . 

I 

8 

— 

— 

— 

— 

— 


— 

46.5 

44 

44 44 

1 



— 

— 

— 

— 

— 

— 

400 

2846.7 

44 

common mortar.. 

1 










2579.2 

44 

beton agglomere. 

— 

I 

— 

— 

— 

— 

4 

— 

— 

72 

727-3 

44 

common mortar.. 


1 









io 4 - 7 


* Vide Treatise on Coignet Beton, p. 28, et seq. New York, 1871 















































624 


APPENDIX. 


Standard Dimensions of Bolts, with Hexagonal Heads 

and Nuts. 


Diameter 
of bolt 
‘n inches. 

No. of 

V threads 
per in. of 
length. 

Breadth 
of head, 
in inches. 

Thickn’ss 
of head 
in inches. 

Breadth 
of nut 
in inches. 

Thickness 
of nut 
in inches. 

Weight 
of round rod 
# per foot 
in pounds. 

"Weight of 
head and nut 
in pounds. 

I 

¥ 

20 

3 

¥ 

I 

¥ 

3 

¥ 

5 

T(T 

• >653 

.017 

5 

T 6" 

l8 

1 

2 

5 

T¥ 

1 

2 

3 

¥ 

• 2583 

•°33 

3 

¥ 

l6 

5 

¥ 

3 

¥ 

5 

¥ 

7 

T¥ 

• 3720 

•057 

7 

T¥ 

14 

I I 
T¥ 

7 

T¥ 

I I 
T¥ 

1 

2 

• 5 o6 3 

.087 

i 

13 

3 

4: 

1 

2 

3 

9 

T¥ 

.6613 

. 128 

T 5 

12 

7 

¥ 

9 

T 5 

7 

¥ 

5 

¥ 

•8370 

. I90 

5 

¥ 

II 

I 

5 

¥ 

I 

I I 

T¥ 

1 -°33 

. 267 

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¥ 

IO 

I ¥ 

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¥ 

*¥ 

I 3 

T¥ 

I.488 

•43 

7 

¥ 

9 

T ¥ 

7 

¥ 

J ¥ 

rf 

2.025 

•73 

I 

8 


I 

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IT¥ 

2.645 

1.10 

i* 

7 

T t 

J ¥ 


. 3 

lT¥ 

3 • 348 

1.60 

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if 

I ¥ 

IfV 

4-133 

2.14 

T ¥ 

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r\ 1 

2 ¥ 

ixV 

5.001 

2-95 

4 

6 

0 1 

2 ¥ 

4 

~I 

2 4T 


5-95 2 

3-78 

T 5 

J ¥ 

5* 

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J ¥ 

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y I I 

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2 ¥ 

t 13 

J T¥ 

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4 } 

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10.58 

8-75 

«I 

4 \ 

3l 

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2 ¥ 

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13-39 

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16.53 

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20.01 

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APPENDIX. 


625 


General Water-works, Statistics, 1880. 


Cities. 

Population in 

1880. 

Average daily 

Consumption. 

Annual 

Revenue. 

Miles of Pipe. 

No. of Meters. 

Albany, N. Y. 

90,903 

6,363,210 

$145,404 

77 

12 

Alleghany, Pa. 

78,682 

10,000,000 

168,000 

60 

I 

Brooklyn, N. Y. 

566,577 

30,674,761 

977,703 

352 

1,085 

Boston, Mass. .. 

362,535 

35.9OO.OOO 

1,044,780 

500 

1,219 

Baltimore, Md. 

332,190 

23,000,000 

606,879 

277 

524 

Buffalo, N. Y. 

I 54-765 

16,369,802 

216,214 

102 

• • • 

Cambridge, Mass. 

52,669 

2,474,616 

177,430 

85 

156 

Cincinnati, Ohio. 

255.708 

19 , 476,739 

499,857 

189 

545 

Cleveland, Ohio. 

155-946 

10,180,000 

203.379 

125 

402 

Chicago, Ill. 

503.304 

57,384.376 

961,051 

461 

2,113 

Columbus, Ohio. 

5 L 644 

2 , 159,327 

44,572 

44 

534 

Detroit, Mich. 

116,027 

15,170,000 

380,684 

209 

29 

Hartford, Conn. 

42,569 

4,000,000 

121,281 

72 

99 

Indianapolis, Ind. 

75.056 

4,000.000 

70,940 

43 

25 

jersey City, N. j. 

120,728 

14,916,825 

249.641 

153 

4 i 

Louisville, Ky. 

126,566 

6,567,141 

187,708 

no 

228 

Lawrence, Mass. 

39,068 

1 861,363 

62.670 

42 

272 

Lowell, “ . 

59,340 

2,252,197 

118,800 

63 

708 

Lynn, “ . 

38,376 

1,238,290 

79,899 

57 

121 

Milwaukee, Wis. 

115,578 

10,604,000 

129,505 

86 

• . . 

Minneapolis, Minn. 

48,323 

3,010,591 

20,819 

19 

• • • 

Manchester, N. H . 

32,458 

1,180,930 

57,264 

33 

280 

Montreal, Canada. 

145.OOO 

9,691,901 

364,475 

133 

305 

New Orleans, La. 

216,090 

9,000,000 

100,000 

69 

. . . 

New York, N. Y. 

1,206,577 

95,000.000 

1,560,599 

503 

4,002 

Newark, N. j. 

136,400 

9,390,000 

312,649 

136 

. • • 

New Haven,'Conn. 

62,861 

5,100,000 

131,580 

98 

13 

Philadelphia, Pa. 

874,542 

57,707,082 

1,415.477 

746 

. • • 

Pittsburgh, Pa. 

156,389 

16,021,624 

302,000 

in 

.. . 

Poughkeepsie, N. Y. 

20,207 

1,403,292 

19,379 

16 

122 

Providence, R. I. 

104,760 

3 , 547-264 

247,705 

155 

4,401 

Quebec, P. Q. 

50,000 

2,500,000 

91,000 

• • • 

2 

Richmond, Va. 

63.243 

5,718,053 

74.909 

53 

. . . 

Rochester, N. Y. 

87,057 

5,607,000 

72,659 

113 

... 

San Francisco, Cal. 

233 959 

13,824,000 

1,300,000 

178 

5,180 

St. Louis, Mo. 

333,577 

25,124.000 

660,280 

212 

573 

Syracuse, N. Y. 

52,210 

4,000,000 

68,000 

42 

• • • 

Troy, N. Y. 

56,747 

5,000,000 

61,080 

40 

• • • 

Toledo, Ohio. 

53,635 

3,270,873 

26,124 

47 

• • • 

Toronto, Canada. 

86,445 

4,787,000 

169,245 

113 

50 

Washington, D. C. 

147,307 

26,000,000 

69,459 

175 

... 

Worcester, Mass. 

58,040 

3,000,000 

84.326 

80 

3,791 

Wilmington, Del. 

42,499 

3,564,856 

67,638 

52 

... 

Yonkers, N. Y. 

18,892 

860,000 

22,162 

23 

402 




























































626 


APPENDIX 


Comparative Water-works Statistics, 1880. 


• 

Cities. 

Average daily con¬ 
sumption per cap¬ 
ita. 

Annual receipts per 

capita. 

Annual receipts for 

each million gal¬ 

lons daily water¬ 
age. 

Miles of pipe for 
each thousand in¬ 
habitants. 

Meters for each 

thousand inhabi¬ 

tants. 

Cost of pumping a 

million gallons 100 

feet high. 

Albany, N. Y . 

Galls. 

70. 

$i -59 

£22,850 

.847 

•13 

$... 

Alleghany, Pa . 

127. 

2.14 

16,800 

.762 

.0127 

• • . 

Brooklyn, N. Y . 

54-14 

1 . 72 

31.873 

.621 

I.92 

6.38 

Boston, Mass. 

99.02 

2.88 

29,102 

i -37 

3-36 

• • • 

Baltimore, Md. 

69.24 

1.83 

26,386 

•833 

i -57 

• • • 

Buffalo, N. Y . 

105-77 

1 -39 

13,208 

•659 

• • • 

. . . 

Cambridge, Mass . 

47 - 

3 -i8 

71,700 

1.613 

2.960 

• • • 

Cincinnati, Ohio . 

76.16 

i -95 

25,664 

•739 

2.13 

5-58 

Cleveland, Ohio . 

65.28 

1.29 

19,880 

.800 

2-57 

4.64 

Chicago, 111 . 

114.01 

1.91 

16,747 

• 9 X 5 

4.19 

5-42 

Columbus, Ohio . 

41.81 

0.86 

20,641 

.852 

1.03 

8.00 

Detroit, Mich . 

130.74 

3.28 

25,094 

1.80 

• • • 

• . • 

Hartford, Conn . 

93-0 

2.84 

30,320 

1.69 

2.32 

• . . 

Indianapolis, Ind . 

53-3 

o -94 

17-735 

•573 

•332 

• • • 

Jersey City, N. J. . ... 

123-55 

2.07 

16,802 

1.26 

•339 

7.84 

Louisville, Ky . 

51.88 

1.48 

28,583 

. 869 

1.8 

5-76 

Lawrence, Mass . 

47.65 

1.60 

33,669 

1.07 

6-94 

4.71 

Lowell “ . 

37-95 

2.00 

52,752 

1.06 

11.9 

5-25 

Lvnn, “ . 

32.26 

2.08 

64.524 

1.47 

3-15 

5-36 

Milwaukee, Wis . 

91.74 

1 . 12 

12,213 

•745 

• • • 


Minneapolis, Minn . 

62.30 

o .43 

6,915 

3-93 

• . . 


Manchester, N. II. 

36-38 

1.76 

48,491 

1.01 

8.62 


Montreal, Canada . 

65-53 

2.51 

37 , 6 < 7 

.916 

2.09 

12.30 

New Orleans. La . ... 

41.6 

0-45 

11,hi 

• 3 i 9 

• • • 


New York, N. Y. 

78.73 

1.29 

16,427 

.416 

3 - 3 i 


Newark, N. I. 

68.63 

2.28 

33.306 

•997 

• • • 


New Haven, Conn . 

81.13 

2 09 

25,800 

1.56 

.206 


Philadelphia, Pa . 

65-9 

1.61 

24.528 

.868 

• • • 

5-51 

Pittsburgh, Pa . 

104.5 

i -93 

18,854 

•709 

... 


Poughkeepsie, N. Y . 

69.47 

0-95 

13,810 

.791 

6.03 


Providence, R. I. 

33-86 

2.36 

69,830 

1.48 

42. 

5.85 

Ouebec, P. O. 

50 - 

1.82 

36,400 

• • . 

.04 


Richmond, Va. . 

90.41 

1.18 

13,100 

.838 



Rochester, N. Y . 

64.40 

0.83 

12,957 

1.29 

• • • 


San Francisco, Cal . 

59 - 

5-56 

94,047 

. 761 

24-833 


St. Louis, Mo . 

75-31 

1.97 

26,281 

•635 

i -7 

5 - 35 

Syracuse, N. Y . 

76.61 

1.30 

17,000 

. 804 

... 

Troy, N. Y . 

Toledo, Ohio . 

88.11 

60.98 

1.07 

0.48 

12,216 

7.987 

•704 

.878 

... 

5 77 

Toronto, Canada . 

55 30 

i -95 

35,342 

1.30 

•57 

Washington, D. C . 

176.50 

o -47 

2.671 

1 . 12 



Worcester, Mass . 

51.68 

i -45 

28,107 

i -37 

6-53 


Wilmington, Del . 

83.88 

i -59 

18,974 

1.22 


4.88 

Yonkers, N. Y . 

45-52 

1.17 

25,770 

1.21 

21.2 

6-39 




































































APPENDIX 


627 


General Water-works Statistics, 1882. 


Cities. 

Number of 

Fire Hydrants. 

Number of 

Meters in use. 

Annual Reve¬ 

nue from Meters. 

Per cent, of con¬ 

sumption 
through Meters. 

Price of Water, 
per 

1,000 gallons. 

Number of Taps 

in use. 

Percentage of 
Taps metered. 




DOI.L. 


CENTS. 



Attleboro, Mass. 

73 

108 

2,000 

• • • 

40 

380 

28. 

Boston, Mass. 

5,032 

2,650 

383,62s 

13.06 

20 to 30 

60,000 

4.04 

Baltimore, Md. 

892 

677 

62,708 

IO.42 

Spcl. 

• • • 

• . • 

Brooklyn, N. Y.... . 

2,970 

1,516 

198,178 

II.46 

Jo .33 

64 T 77 

2.36 

Buffalo, N. Y. 

1,400 

140 

80,000 

• • • 

• • • • 

13,400 

• • • 

Binghamton, N. Y. 

175 

80 

5,024 

3 - 

6 to 25 

1,935 

4 - 

Chicago, Ill. 

3,825 

2,310 

363,000 

11. 

8 to 40 

78,840 

3 - 

Cambridge, Mass. 

596 

156 

42,466 

26. 

20 

7-725 

2. 

Cleveland, Ohio.... . 

1,264 

702 

101,192 

20.57 

6.66 to 13.33 

12,923 

5-9 

Cincinnati, Ohio. 

900 

780 

75,000 

n. 18 

9 

24.500 

3-2 

Columbus, Ohio. 

363 

546 

27,969 

•25 

7 to 20 

2,288 

•25 

Detroit, Mich. 

872 

27 

7,000 

• • • 

10 

26,000 

. . • 

Elmira, N. Y. 

146 

183 

. 

• • • 

10 to 50 

900 

. 20 

Fall River. Mass. 

655 

1,966 

49,018 

23.06 

30 

3.12063.08 

Fitchburg, Mass. ... . 

203 

150 

5-940 

• • • 

10 to 50 

i,442|io. 

Grand Rapids, Mich. 

1,296 

352 

i r ,000 

• . • 

15 to 30 

1,032 

32 . 

Holyoke, Mass. 

177 

105 

9,839 

• • • 

5 to 15 

1-493 

• • • 

Hoboken N. J. 


42 

23,000 

10. 

12 to 15 

3.000 

1.5 

Jacksonville, Fla. 

102 

160 

3 -II 5 

20. 

15 to 30 

250 

6.4 

Jersey City, N. J. 

i, 4 i 5 

281 

194,737 

25 - 

• • • • 

• • • 

• • • 

Kansas City, Mo. 

393 

141 

20,640 

7-5 

15 to 35 

2,788 

•5 

Louisville, Ky. 

365 

273 

84,390 

• • . 

6 to 15 

7,947 

3-5 

Lowell, Mass. 

727 

1,090 

43.000 

24. 

.... 

6,200 

21. 

Lawrence, Mass. 

470 

421 

19,750 

. . • 

20 to 25 

3,653 

11 • 5 

Lynn, Mass. 

49S 

156 

13,358 

9.07 

25 and Spcl. 

5 , 44 i 

3 - 

Meriden, Conn. 

180 

64 

10,862 


10 to 25 

2.000 

• • • 

Manchester, N. H. 

339 

400 

L 333 

14. 

26.66 

2,140 

18. 

Milwaukee, Wis. 

794 

102 

44.273 

10. 

4.6 to 20 

7,974 

• • • 

New Haven, Conn. 

650 

20 

4,500 

• • • 

15 to 30 

7,000 

3 . 

Newton, Mass. 

344 

664 

13,000 

17.07 

35 

2 , 37 i 

28. 

New York, N. Y. 

6,944 

6,817 

186,600 

14. 

13-33 

85,000 

8, 

Newark, N. J. 

i,i 97 

252 

36,021 

8.9 

• • • • 

12,676 

84,5 

New Brunswick, N. J.... 

166 

68 

13-724 

24 . 

• • • • 

1,330 

5 - 

Poughkeepsie, N. Y. 

286 

176 

4,682 

6. 

10 to 20 

i ,436 

12.2 

Providence, R. I. 

1,186 

5,279 

• ••••• 

• • • 

15 to 30 

io ,357 5 i- 

Pawtucket, R. I. 

965 

1,600 

• ••••• 

• • • 

6 to 30 

3,000 50. 

Rochester, N. Y. 

1,050 

639 

46,000 

30 . 

12.5 to 30 

12,000 

5-3 

San Francisco, Cal. 

L 39 6 

5,846 

464,400 

• . • 

• • • • 

23,000 20. 

Salem. Mass. 

154 

134 

9,257 

• . . 

13.5 to 20 

4,700 

2.03 

Springfield, Mass. 

424 

no 

2,870 

2. 

30 and Spcl. 

3,500 

3 - 

St. Louis, Mo. 

1,980 

1,218 

222,400 

• . • 

12.5 to 30 

28,000 


Toledo, Ohio. 

361 

no 

2,000 

8.7 

8 to 20 

1,853 

20. 

Taunton, Mass . 

367 

401 

12,139 

38. 

12.5 to 25 

2,062 

19. 

Waterbury, Conn. 

180 

84 

9,000 

• • • 

5 to 30 

2,217 

• • • 

Worcester, Mass. 

690 

4,709 

82,914 

.07 

15 to 25 

6,061 

77 . 

Yonkers, N. Y. 

263 

605 

14,945 

48. 

16 to 40 

i,i 33 

• • • 














































































628 


APPENDIX. 


Stand-Pipe Data. 


LOCATION. 

Diameter. 

Feet. 

Height. 

Feet. 

Thickness 
of base. 
Inches. 

Thickness 
of top. 
Inches. 

Wichita, Kan. 

2 T 
z 2 

1 5 0 

1 

2 

6 

TF 

Milwaukee, Wis. 

5 

80 

1 

2 

1 

Henderson, Ky. 

5 

80 

1 

2 

I 

T 

Catasauqua, Pa. 

Toledo, Ohio. 

5 

100 

3 

'8 

I 

T 

5 

224 

1 

2 

I 

Erie, Pa. 

5 

233 

3 

? 

I 

T 

Allentown, Pa.. . 

6 

ss 

3 

~S 

I 

Bristol, Pa. 

6 

140 

7 

T<T 

5 

T 5 

New York City, High Service 

6 

l S° 

1 

2 

I 

J 

Joliet, Ill. 

7 

io 5 

5 

8 

I 

T 

Mt. Pleasant, la. 

IO 

80 

5 

s 

3 

If 

Sandwich, Ill. 

12 

100 

I 

" 5 " 

3 

ttt 

Levvisburgh, Pa. 

12 

13° 

I 

"T 

1 

n; 

Maquoketa, la. 

I2t 

80 

7 

Tef 

1 

Freeport, Ill. .. 


88 

5 


Lincoln, Neb. 

18 

75 

I 

3 

TTT 

Charleston, S. C.. 

18 

76 

I 

A 


Yonkers, N. Y. 

18 j 

21 

I 

9 

3 

T 7 Z 

Princeton, N. J. 

20 

60 

3 

~Q 

T 

~T 

Perth Amboy, N. J.. .. 

20 

7 1 

5 

it 

I 

Alliance, O . 

20 

80 

5 

IT 

3. 

Wilmington, N. C. 

20 

90 

0 

7 

8 

3 

T 5 - 

Dedham, Mass. 

20 

103 

5 

5 

South Abington, Mass. 

20 

io 5 

O 

5 

I 6 
_5 

Nantucket, Mass. 

2 5 

15 

8 

I 

T 6 

Fremont, O. 

2 5 

100 

4 

5 

3 

Atlantic City, N. J. 

2 5 

132 

8 

5 

■g 

I 6 

3 

nr 

Sandusky, O . 

11 

180 ) 
22 9 f 

7 

Tf 

3 

Newton. Kan. 

3o 

76 

5 

if 

I 

x 

Springfield, O. 

30 

112 

7 

■g - 

A 

Franklin, Mass. 

40 

35 

3 

"S’ 

I 

Wakefield, Mass. 

40 

60 

1 

5 

N. Attleborough, Mass. 

40 

62 

1 

1 

2 

1 & 

5 

T7T 

















































APPENDIX. 


629 


Weights of Lead and Tin Lined Service-Pipes. 


Calibre. 

AAA. 
Weight 
per ft. 

AA 
Weight 
per ft. 

A. 

Weight 
per ft. 

B. 

Weight 
per ft. 

Q 

Weight 
per ft. 

D. 

Weight 
per ft. 

D. Light. 
Weight 
per ft. 

E. 

Weight 
per ft. 

E. Light. 
Weight 
per ft. 

I?iches. 

Lbs. 

Lbs. 

Lbs./ 

Lbs. 

Lbs. 

Lbs 

Lbs. 

Lbs. 

Lbs , 

3 

8 

1-5 

1-3 

I . 12 

I 

I .06 

0.62 

— 

0-5 

— 

1 

¥ 

3 

2 

i-75 

1.25 

I 

O .81 

— 

0.7 

O .56 

5 

¥ 

3-5 

2-75 

2-5 

2 

1-75 

1-5 

I .25 

I 

0-75 

3 

¥ 

4-5 

3-5 

3 

2.25 

2 

1.75 

i-5 

I .25 

I 

I 

6 

4-75 

4 

3.25 

2-5 

2 

— 

1-5 

— 


6 75 

5-75 

4-75 

3-75 

3 

2-5 

— 

2 

— 

4 

9 

8 

6.25 

5 

4-25 

3-5 

— 

3-25 

— 

2 

10.75 

9 

7 

6 

5.25 

4 

— 

— 

— 


A manufacturer’s circular states that the following quanti¬ 
ties of water will be delivered through 500 feet of their pipes, 
of the respective sizes named, when the fall is ten feet: 


Calibre. 

§ inch. 

| inch. 

| inch. 

f inch. 

1 inch. 

Ip inch. 

Gallons per minute... 

•343 

.798 

1.416 

2.222 

4.600 

6.944 

Gallons per 24 hours.. 

576 

1150 

2040 

3200 

6624 

10000 


A j-inch clean service-pipe connected to a -J-inch tap 
under a hundred feet head, will deliver at the sink, through 
a common compression bib, ordinarily about three pails of 
water, or say 8.25 gallons, or 1.1 cu. ft. of water per minute. 

Lead is more generally used for service-pipes than any 
other material, but wrought-iron pipe, lined and coated 
with cement, or with a vulcanized rubber composition or 
sundry coal-tar compositions and enamels, have been used 
to a nearly equal extent within a few years past. Block- 
tin pipe, tin-lined pipe, and galvanized iron pipe, have been 
used also to a limited extent. 

































630 


APPENDIX. 


Safe Weights of Lead Service Pipes. 

Good lead pipes have an ultimate cohesion of about 
2000 lbs. per square inch. The effect of the water ram 
when the house faucets are suddenly shut is not quite as 
severe on services as it is on the risers and fixtures in the 
house. Fifty per cent, of the pressure is a fair allowance 
for the ram on services, if an additional coefficient of safetv 
of 5 or .2 s is taken to cover the limit of elasticity and ordi¬ 
nary weaknesses. 

On this basis we have formulas for thickness t and 
weight w , 

. _ 1 ,5pr _ 7 ,6pr 
.2 $ ~ s ’ 

i " ~ 

w = (d+t) x tx 7T x 12" x .411, 

in which p = pressure in lbs. per sq. inch. 

= .434 head in ft. 

r = internal radius of pipe, in inches. 
d — internal diameter of pipe, in inches. 
t — thickness of pipe shell, in inches. 
t r = 3.1416. 

s = ultimate cohesion of lead, mean, 2000 lbs. per 
sq. in. 



APPENDIX. 


631 


Weights for given Pressures of Water. 


, Head, of Water in Feet. 

75 | ioo | 125 I 150 | 175 I 200 | 225 1 250 | 275 | 300 

Pressure of Water in Pounds. 

32.55 I 43‘4° I 54-25 I 65.xo I 75.95 I 86.80 I 97.65 I 108.50 I 119.35 I 130.20 

Weights of Lead Pipes per foot, in Pounds. 


Diameter, y 2 " . 

X 

% 

/a 

% 

34 

X 

X 

% 

I 

x>4 

“ */s" . 

Vs 

X 

% 

X 

% 

I 

d/s 

'X 



“ X" . 

X 

X 

% 

I 

iJ4 

04 

134 

*X 

2 

234 

“ x // 

% 

d/a 

1 14 

04 

2 

2?4 

• 2 % 

3 

3 % 

3% 

“ iK" . 

x34 

m 

214 

2 % 

334 

3X 

4/4 

aX 

5 '4 

5% 

“ 1 ‘A" . 

2 

2'/2 

3*4 

3% 

A% 

sX 

6 

6X 

7 >4 

814 


These weights should be increased somewhat in the 
house plumbing. 





















632 


APPENDIX. 


RESUSCITATION FROM DEATH BY DROWNING. 

“Persons may be restored from apparent death by 
drowning, if proper means are employed, sometimes when 
they have been under water, and are apparently dead, for 
fifteen or even thirty minutes. To this end— 

1. Treat the patient instantly, on the spot, in the open 
air, freely exposing the face, neck, and chest to the breeze, 
except in severe weather. 

2. Send with all speed for medical aid, and for articles 
of clothing, blankets, etc. 

I. To Clear the Throat. 

3. Place the patient gently on the face, with one wrist 
under the forehead. 

(All fluids, and the tongue itself, then Ml forwards, and 
leave the entrance into the windpipe free. 

II. To Excite Respiration. 

4. Turn the patient slightly on his side, and 

(I.) Apply snuff, or other irritant, to the nostrils ; and 

(II.) Dash cold water on the face, previously rubbed 
briskly until it is warm. 

If there be no success, lose no time, but 

III. To Imitate Respiration. 

5. Replace the patient on the face. 

6. Turn the body gently but completely on the side, and 
a little beyond, and then on the face alternately, repeating 
these measures deliberately, efficiently, and perse- 
veringly, fifteen times in the minute only. 

(When the patient reposes on the chest, this cavity is 


APPENDIX. 


633 


compressed by the weight of the body, and expiration 
takes place ; when it is turned on the side, this pressure is 
removed, and inspiration occurs.) 

7. When the prone position is resumed, make equable 
but efficient pressure along the spine, removing it immedi¬ 
ately before rotation on the side. 

(The first measure augments the expiration, and the 
second commences inspiration.) 

TV. To Induce Circulation and Warmth, continue 

these Measures. 

8. Rub the limbs upwards, with firm pressure and 
energy, using handkerchiefs, etc. 

9. Replace the patient’s wet covering by such other cov¬ 
ering as can be instantly procured, each bystander supply¬ 
ing a coat or a waistcoat. Meantime, and from time to time, 

Y. Again, to Excite Inspiration, 

10. Let the surface of the body be slapped briskly with 
the hand; or 

11. Let cold water be dashed briskly on the surface, 
previously rubbed dry and warm. 

Avoid all rough usage. Never hold up the body by the 
feet. Do not roll the body on casks. Do not rub the body 
with salts or spirits. Do not inject smoke or infusion of 
tobacco, though clysters of spirits and water may be used. 

The means employed should be persisted in for several 
hours, till there are signs of death.” 


INDEX 


The figures refier to the pages. 


A. 

Acceleration of motion, 185. 

Adirondack watershed, iox. 

Adjustable effluent pipe, 364. 

Advantages of water supples, 29. 

Air, resistance of, to a jet, 190. 

Air valves, 523. 

“ vessels, 564, 565. 

Ajutage, an, 213. 

“ inward projecting, 218. 
vacuum, 214. 

Algae, fresh water, 129. 

Analyses of lake, spring, and well waters, 117. 
‘ c “ mineral waters, 143. 

“ “ potable waters, table, 117. 

“ “ river and brook waters, 118, 120. 

Analysis of impure ice, 136. 

Anchoring stand-pipes, 588, 589, 599. 

Angles of repose of masonry, 396. 

Angular force graphically represented, 175. 

Apertures, sluice, 201, 202, 203. 

Aquatic life, purifying office of, 132. 

“ organisms, 131. 

Arago’s prediction at Grenelle, 106. 

Areas of sluice valves, 360. 

Artesian wells, 105, 106, 108. 

“ “ temperature of, table, 127. 

Artificial clarification of water, 159. 

“ gathering areas, 100. 

“ pollution of water, 152. 

“ storage “ “ 84,93, 95, 98, 99. 

Asphaltum bath for pipes, 475, 487, 490. 

Atlantic coast rainfall, 53. 

Atomic theory, 162. 

Attraction, capillary, 296. 

Atmospheric impurities of water, 122. 

“ pressure, 182. 

Average consumption of water, 44. 

B. 

Basins, clear water, 550. 

“ fitter, 536, 537 , 548, 55 i, 553, 555. 

“ infiltration, 537. 

“ settling, 550. 

Batters, front of masonry, 383, 385, 387, 424. 

Beams, cylindrical, strength of, 600. 

Bends and branches, 272, 275, 478, 485. 

“ coefficients for, table of, 274. 

Blow-off valves, 513. 

Boiler at Newport water works. 580. 

Boilers, 577, 578, 580. 

Bolts and nuts, standard dimensions, 624. 

Bolts in flanges, table of, 462, 

Bolt-holes, templet for, 460. 

Boyden’s hook gauge, 297. 

Branches and bends, 272, 478, 484. 
composite pipe, 484. 

“ formula for flow through, 275. 

British water supplies, 37. 


Bucket-plunger pump, 557, 567. 

Building stones, strength of, 404. 

Bursting pressure, 232. 

C. 

Caloric, influence of, 163. 

Canal banks, 370. 

“ in side hill, 370. 

“ miner’s, 375. 

“ open, 370. 

“ revetments and pavings, 371, 374, 

“ slopes, 371, 374. 

“ stop gates, 373, 374. _ 

Canals and channels, velocities in, 302, 303, 304, 
307, 308, 310, 312, 314, 318, 320, 325, 326, 330, 
373- 

Canals and rivers, observed flows in, table of, 


307, 373- 
id 


44 

44 


Canals and rivers, coefficients for flow in, 308. 
irrigation, 370, 372, 373, 375. 
noted, 373. 

water supply, 370, 373, 37s. 

Cantilever, strength of cylindrical, 599,600,601. 
Capacity for filter beds, 552, 554, 

Capillary attraction, 296. 

Cast-iron pipes, 451. 

“ “ weights of, 465, 468, 469. 

Cast socket on wrought pipe, 483. 

Casting of pipes, 452. 

Cement joints of pipes, 482. 

*‘ lined pipes, 479. 

“ lining of pipes with, 481. 

“ mortar for lining and covering pipes, 
487. 

“ tensile strength, 623. 

Census statistics, 31. 

Central rain system, 49. 

Chamber, effluent, 358. 

“ influent, 366. 

“ walls, 369. 

Chandler’s, Prof., remarks on wells, 140. 
Channels, coefficients for, 308. 

“ depths and relative volumes 

velocities, 328. 

“ experimental flow in, 307, 309, 

214. 415, 417, 321, 323, 326, 326^. 
flow in, experimental data, 306. 

“ open, 299, 370, 373, 375. 
formulas for flow, table, 310. 
inclination in, 304. 
influences controlling flow in, 316. 
mean velocities, 312, 314, 316, 318, 
3 X 9- „ 

ratios of surface to mean velocity, 


and 


3*2l 


41 

44 

44 

44 

44 

44 


surface velocities, 313. 
velocity of flow in, 303, 304, 307, 308, 
310. 3x4, 318. 321, 328. 
velocities of given films, 311. 
water supply, protection of, 431. 










INDEX. 


635 


•Characteristics of pipe metals, 470. 

Charcoal clarification ot water, 535, 537. 

“ filters, 536. 

Check valve, 367, 525. 

Chemical clarification, 532. 

Choice of water, 587. 

Cities, families in various, 32. 

persons per family in various, 32. 

“ population of various, 32. 

“ water supplied to, 35, 36, 37. , 
Clarification of water, artificial, 159. 532, 535, 
537 i 547 - 

Clarification of water, charcoal, 535, 537. 

chemical, 532. 
natural, 149, 530, 532. 
Cleaning of filter beds, 553. 

Clear water basins, 550. 

Climate effects, rainfall, 47. 

Coal required for pumping, 581. 

Coating (asphaltum) pipes, 475, 487, 490. 
Cochituat.e basin, rain upon, 72. 

Coefficients, compound tubes, 219, 220. 

convergent tubes, 217. 
c ', table of, 271. 
experimental, 198. 

“ table of, 237. 

for channels, Kutter’s, 305. 

“ circular orifices, 196, 199, 203. 
“ current meters, 325, 326, 326a. 
“ flow in conduits. 444. 

“ hydrometers, 325. 

“ pipes, table of, 242. 

“ rectangular orifices, 198, 200, 
201, 202, 205, 206. 

“ service pipes, 528. 

“ short tubes, 214, 217, 218, 219, 
220, 227, 228. 

“ sluice apertures, 201, 202, 203, 
205, 206. 

“ various forms of tubes, 215, 
218, 219, 220, 221. 

“ weir formulas, 287, 288. 

“ wide crested weirs, 294. 
formulas for pipes, 236, 242, 267, 
271. 

from Castel, 200. 

“ Eytelwein and d’Aubuis- 
son, 256. 

“ General Ellis, 201. 

“ L’Abbe Bossut, 199. 

“ Lespinasse, 201. 

“ Michelotti, 198. 

“ Prony, 225. 

“ Rennie, 199. 

increase of in short tubes, 213. 
m, 234, 247. . . 

mean, for smooth and foul pipes, 
248, 249, 267. 

of efflux, factors of, 197, 208. 

“ table of, 227. 
of entrance of jet, 267. 

“ flow from channels, 305, 307, 
308, 329. 

“ flow in pipes, 236, 242, 248, 495. 
“ friction of earth-work, 345. 

“ “ table of, 495. 

“ issue from short tubes, 218. 

“ masonry friction, 396. 

“ velocity and contraction of 
orifice jets, 208. 
practical application of, 197. 
range of, 222. 
resistance in bends, 274. 
tables of, for pipes, 236, 242, 248, 
495 - 

variable values of, 210. 
Coffer-dams, 430 

Combined reservoir and direct systems, 525. 
Commercial use of water, 34. 


Compensation flow, 86. 

“ to riparian owners, 94. 

Composite branches, pipe, 484. 

Composition of water, the, 112. 

Compound tubes, 218, 220. 

“ coefficients for, 220. 
Compressibility and elasticity of water, 167. 
Concrete conduit, a. 438. 

“ foundations, 368. 

“ “ for pipes, 487. 

“ paving, 355. 

“ proportions of, 368. 

“ revetments, 429, 430. 

“ wall, 338, 348. 

Conduit arch, thrust of, 437. 

“ data, 445 . 

“ masonry to be self-sustaining, 437. 

“ of concrete, 438. 

“ “ wood, 439, 441. 

“ shells, 434 
Conduits and pipes. 223. 

“ backing of, 438. 

“ capacities of noted, 445. 

“ coefficients for, 444. 

examples of, 74, 431, 435, 438, 439,445, 

“ exposure to frost, 437. 

“ formulas for flow in, 442, 443, 445. 

“ foundations for, 433. 

“ locked bricks for, 435. 

“ masonry. 431. 

“ mean radii of, 441, 442. 

“ protection from frost, 436. 

“ stop-gates in, 436. 

“ transmission of pressure in, 436. 

“ under pressure, 435, 439. 

“ ventilation of, 434. 

Confervse, 129. 

Construction of embankments, 348. 

“ “ filter beds, 548. 

Consumption of water, 34, 43, 503. 

Contents of pipes. 504. 

Core of an embankment, 348. 

Cornish pump, 557, 563. 

Costs of pumping water, 574, 575. 

Crib-work foundations, 385. 

“ weir, 384. 

Croton basin, rainfall upon, 72. 

“ Dam, 94. 

“ Aqueduct, 74, 431, 445. 

Curbs, stop-valve, 515. 

Current meters, 322, 325, 326, 326a. 

“ meter rating. 325, 325a, 326. 
Curved-face wall, 421. 

Cut-off wall embankment, 338, 348. 

Cycle, low, rainfalls, 69, 77, 78. 

Cylindrical cantilevers, strength of, 599, 600. 

“ penstock, 440. 

“ pressures in, 593. 

“ thickness of, 448, 450, 486, 488, 489. 

“ tubes, 222. 

D. 

Dams, aprons of. 383, 387, 388. 

“ caps, 386. 

“ discharges over, 290, 298a, 378, 380, 381, 
388. 

“ forms of, 94, 382, 384, 391. 

“ ice thrust on, 386. 

“ thickness of, 387. 

Darcy-Pitot tube gauge, 322. 

Data from existing conduits, 445. 

Debris, floating, 530. 

Decimal parts of an inch and foot, 457. 
Decomposing organic impurities, 127. 
Densities and volumes of water, relative, 164. 
Depths of pipes, 501, 502. 

“ on weirs, 228, 290, 298a. 

Desmids, in fresh ponds, 129. 


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636 


INDEX. 


Details of stop-valves, 513. 

Diagonal force, 175. 

Diagrams of pumping, 42. 

“ “ rainfall, 55, 57, 551. 

44 “ stand-pipe stabilities, 597. 

Diameter of sub-mains, 507. 

“ supply-main, 500. 

Dimensions of existing canals, 373. 

“ 44 filter-beds, 554. 

“ “ retaining walls, 420. 

Direct pressure system, 525, 590. 

Discharges of pipes, 498, 500. 

“ over waste-weirs, 378,381. 

“ “ weirs, 288, 290, 298a. 

Distribution pipes, 493, 495, 503, 505, 506, 508. 
Domestic draught of water, 34, 508. 
Drainage from given areas, 67, 75. 

Draught, variations in, 41. 

Drowning, resuscitation, 632. 

Duplicate pumping machinery, 590. 
Duplication in pipe systems, 510. 

Duty of pumping-engines, 574, 576, 580, 583. 
Dwellings in various cities, 32, 33a. 

Dykes, canal and river, 371. 


E. 


Earth and rock, porosity of, 102. 

“ embankments, 333, 347, 348, 353, 370. 

44 evaporation from, 89. 90. 

“ pressures against walls, 408. 

Eastern coast rain system, 50. 

Economy of high duty of pumping-engines, 
579 i 581. 

“ 44 skillful workmanship, 369. 

Eddies, in weir channels, 292. 

Effect, mechanical, of the efflux, 225. 

Effluent chambers, 358. 

44 pipe, adjustable, 364. 

“ u ice thrust upon, 358. 

Efflux, equation of, 211. 

“ factors of the coefficient, 197. 

“ from pipes, coefficients of, 196, 227. 

“ sluices, 201, 203, 205, 206, 207. 

“ mechanical effect of, 225. 

44 peculiarities of jet, 207. 

“ volume from short tubes, 194, 210, 214. 
Elasticity and compressibility of water, 167. 
Electric current meters, 326, 326a. 

44 meter register, 325a. 

Elementary dimensions of pipes, 504. 
Elements, the vapory, 45. 

Embankment, a light, 353. 

“ core materials, 339, 342, 348, 354, 

359 - 

“ cut-off walls, 330, 338, 348. 

“ example of, 347. 

“ failures, 334. 

“ fine sand in, 353. 

“ foundations, 335, 337, 338. 

“ frost covering, 350. 

“ gate chambers, 357,358. 

masonry faced, 354. 
materials, coefs. of friction, 345. 
44 “ frictional angle of, 


proportions of, 340, 
349 - 

weights of, 341. 
pressures in, 343. 
puddle wall. 351, 354. 
puddled slopes, 352, 356, 370. 
revetted, 149, 354, 370. 
sheet-piling under, 339. 
site, reconnaissance for, 347. 
slope-paving, 350, 355. 
slopes, 344, 345, 350, 355. 
sluices, 355, 356, 358. 
soils beneath, 337. 


Embankment, springs under foundation, 337. 
4 * substructure, 336. 

44 siphon waste-pipe, 358. 

“ test borings at site, 336. 

*• treacherous strata under, 338. 

Embankments, canal, 370. 

effect ot waves on, 388. 

44 Indian, 334. 

“ reservoir, 333. 

Energy of jet, 225, 276. 

England, supply per capita, 37. 

Equation of motion, 186. 

44 “ resistance to flow, 233. 

Equilibrium destroyed, r7o, 300. 

Equivalent heads and pressures of water, 614. 
Errors in application of formulae, 252, 257. 

“ 44 weir measurements, 296. 

Estimates of flow of streams, 78, 94. 

European infiltration, 544. 

“ water supplies. 36. 

Evaporation, effect upon storage, 93. 

“ examples of, 90. 

“ from earth, 89, ito. 

44 44 reservoirs, 94. 

“ “ water, 88, 89. 

“ phenomena, 87. 

“ ratios of, table. 92. 

Evaporative power of boilers, 578, 580. 
Examples of conduits, 431, 438, 439. 

Expansion of water, 164, 166. 

Expansions of pipe metal, 458. 

Experimental channel data, 306. 

“ coefs. for hydrometers, 325. 

“ “ pipes, 236, 241. 

flow in channels, 306, 307, 309, 
312, 314, 315, 317, 321, 323, 326, 
326a. 

“ hose streams, 520. 

Experiments with weirs, 284, 288, 291, 294. 

by Fairbairn on cylindrical 
beams, 600. 


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44 Bossut, 199. 

“ Eytelwein, 220, 222. 

“ Eytelwein’s coefs., 222. 
4 ' Castel, 200, 217. 

“ Couplet, 239. 

“ Darcy, 237, 240. 

“ Du Buat, 238. 

“ Ellis, 201. 


banning, 238. 

“ Lespinasse, 201. 

“ Michelotti, 198. 

“ Pro vis, 198. 

‘‘ Rennie, 199, 239. 

Smith, 236. 

♦with compound tubes, 220. 

44 current meter, 325a. 

44 cylindrical beams, 600. 

4 " orifices, 198, 199, 200, 201. 
44 u short tubes, 217, 219, 220. 

Exposed stand-pipes, 598. 


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F. 

Faced revetments, 429. 

Factors of safety, 449, 451, 453, 485, 4S6, 593. 
failures of embankments, 334. 

14 44 walls, 427. 

Falling bodies, 187, 190. 

Families in various cities, 32. 

Fascine revetments. 371. 

Filter-beds, 547, 548, 553, 553, 554. 

capacity ot, 552, 554. 

44 cleaning of, 553. 

construction of, 548, 551, 554. 
ice upon, 556. 
protection of, 548, 555. 

“ temperature of, 555. 




INDEX. 


637 


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tt 

tt 

44 

44 


44 

44 

41 

44 

44 

44 

44 


Filter-beds, vegetable growth in, 

Filters, Atkin’s, 536. 

Fire draught of water, 34, 506, 508. 510. 

“ extinguishment, reserve for, 44. 
hydrants, 5x0, 516. 5I9 , 521, 522. 
losses, effect of water upon, 26. 
service, 493, 588, 589, 591. 

u head desirable lor, 493. 
supplies, diameteis of pipes for, 510. 

Fish screens, 365. 

Flanges, diameters of valve, 462. 

“ of cast-iron pipes, 462. 

Flash-boards, 378. 

Flashy and steady streams, 71. 

Flexible pipe-joints, 463. 

Floats, double, gauge, 326. 

“ maximum velocity, 328, 
u mid-depth, 326. 

Flood flow, 65, 98. 

“ volumes, 62, 65, 66, 67, 75, 380, 381. 

“ ratios of, to rainfalls, 62. 

“ seasons of, 68. 

Flow, available for consumption, 94. 

“ coefficients of, in pipes, 230, 236, 242, 
248, 495. 

compensation, 86. 

equivalent to given depths of rain, 81. 
from Croton and Cochituate basins, 73. 
44 different surfaces, 77. 

“ Sudbur/ basin, 83a. 
gauged volumes of, 277. 
gravity the cause of, 299. 
in channels, experimental, 306, 307, 309, 
312, 314, 315, 317, 321, 323, 326, 326 a. 
in pipes, frictional head, 225, 233, 250, 
252, 253, 254, 255, 266, 268, 270, 495, 
508, 528. 

in pipes, velocity formulas, 249, 250, 252, 
254, 259. 263, 266, 267, 268, 270, 273. 
in seasons of minimum rain, 69. 
increase and decrease of, 86. 
influence of absorption and evaporation 
upon, 68. 

minimum, mean and flood, 75. 
of streams and channels, 65, 299. 

“ water, 184. 
over a weir, 280. 

per acre and per mile from given rains, 
82. 

periodic available, 69, 101. 
resistance to, in channels, 232, 300. 
sub-surface equalizers of, 70. 
summaries of monthly statistics of, 71. 
through orifices, 194. 

pipes, 223, 495, 508, 560. 
short tubes, 213. 
sluices, pipes and channels, 161. 
Fluctuations of streams, 73, 83«, 101, 319. 
Flush hydrants, 519, 521. 

Foot and inch, equivalent decimal parts of, 457. 
Force, loss of, in pipes, 224. 

44 percussive, of particles, 221. 

Forces, angular. 176. 

“ equivalent, 172. 

“ graphically represented. 175. 

Formula, efflux from an orifice. 196, 209, 211. 

“ “ short pipes, 215. 

for area of sluices, 361. 

“ capacity of air vessel, 566. 

“ coal for pumping, 581. 

“ current meter coefficient, 326. 

“ curved-face walls, 421. 

“ depth upon a weir. 286. 

“ duty of pumping-engines, 576. 

“ earth pressures upon walls, 410, 
412, 4x3, 415, 4x6. 

“ energy of jets, 226. 

“ hydraulic mean depth, 235, 303, 
441. 


44 

44 

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44 

44 

44 

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44 

44 

44 

44 

44 

44 

44 

44 

44 


44 

44 

44 


44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 


44 

44 


44 

44 

44 

44 

44 

44 


44 

44 

44 

44 

44 

44 


Formula for inclination in channels, 304. 

pipe coefficients, 236, 242, 267, 
271. 

1,4 power consumed in pumps, 560, 
561. 

“ power to produce flow in pipes, 
561. 

“ pressure in pipes, 447. 

on submerged walls, 

, . 393 . 394 - 

relative volumes and tempera¬ 
tures of water, 166, 167. 

“ resistance in channels, 301, 303. 

44 submerged orifice, 209. 

14 surcharged pressure walls, 414, 
416, 423. 

“ thickness of walls, 399, 413, 421. 

“ triangular notch weir, 294. 

“ velocity in channels, 303, 304,307, 
3°8, 314, 320, 325, 326. 
volume at given temperature, 
165. 

“ weight of cast pipes, 460, 465, 
467 - 

gravity and motion due to, 186, 187, 
190. 

heights and times of falling bodies, 
186, 187, 190. 
of factor of safety, 593. 

“ M. Chezy, pipes, 252. 

“ power to open sluices, 363, 364. 

“ pressure in cylinders, 448, 593. 

“ resistance of tanks, 589. 

14 weight of anchorage of tanks, 589. 
“ Weisbach, 257. 

44 wind and force on tanks, 588. 
Formulas, coefficients for weir, 284, 287, 288, 
289, 291, 293, 294. 

“ for diameters of pipes, 251, 266, 269, 
270, 498. 

for flood volumes, 66, 67, 320, 380. 

14 flow in conduits, 442, 443. 

44 44 4 4 pipes, 254, 257, 498. 

origin of, 229. 
through bends, 272. 

44 branches, 275. 

44 channels, 303, 304, 

307, 308, 310, 314, 

320, 325, 326. 

44 gauging streams, 320. 

44 head, pipes, 233, 250, 266, 268, 
270. 494. 

lengths ot pipes, 269, 270. 
pipes, various compared, 254. 

44 resistance to flow, 230, 233, 234, 
250, 254, 256, 266, 268, 270, 272, 
275 . 528. 

44 44 shafts, 617. 

44 44 thickness of pipes, table, 466, 

486, 487. 

44 thickness of cast pipes, 453, 454. 
44 44 4 4 wrought pipes, 448, 

450, 486. 

44 44 velocity, pipes, 248, 249, 250, 

259, 266, 267, 268, 270, 272, 498. 
44 44 velocities in channels, 302, 303, 

304 , 307 . 3 ° 8 . 3 xo > 3*2, 314, 320, 
325, 326, 330. 

44 44 volume, pipes, 250, 254, 266, 498. 

44 water ram, 449. 

44 storage ratios, 95, 97. 
weir volumes, 282, 283, 284, 286, 
287, 293, 298a. 379, 380. 

44 44 wide-crested weirs, 293. 

44 manv incomplete, 252. 

44 misapplication of, 316. 

44 of thickness of stand-pipes, 593, 595, 

599, 600. 

44 stability of masonry, 395, 397, 398. 


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638 


INDEX. 


Formulas, velocities and times of falling bod¬ 
ies, 186, 187, 190. 

Foundation, concrete, 386. 

“ embankment, 335. 

“ for pipes, 487. 

“ of conduits, 433. 

“ “ gate-chambers, 367. 

“ “ walls, 395, 406, 407. 

“ under water, 430. 

Foundations, angles. 396, 423. 

“ frictions on, 396. 

“ of stand-pipes, 586. 

Fountain, use of water, 34. 

Francis, Jas. B., experiments with weirs, 284. 
“ tubes. 317. 

Frankland’s defi .ition of polluted water, 137. 

Friction, coefficient of masonry, 396. 

in pipes, 230, 234, 250, 495, 508, 528. 

“ of ice on canals, 372. 

“ “ pumping machinery, 578. 

Frictional head, formulas for, 225, 233, 250, 252, 
253, 254, 255, 266, 268, 270, 495, 508, 528. 

Frost curtain, 367. 

“ disintegration o‘ mortar by, 436. 

“ protection of conduits from, 436. 

Fuel, expense for pumping, 581. 

“ required for pumping, 575. 

Fungi, microscopic, 129. 


G. 

Galleries, infiltration, 539, 540. 

Gate chambers, 357, 367. 

“ hydrants, 522. 

Gates, stop, canals, 374. 

Gauge, Darcy-Pitot tube, 322. 

“ Darcy’s double lube, 322. 

“ double float, 326. 

“ formulas, 319. 

“ hook, Boyden’s, 296, 297. 

“ maximum velocity float, 328. 

“ mid-depth float, 326. 

“ Pitot tube, 320. 

“ rain, 63. 

“ rule, for weirs, 298. 

“ tube, 317. 

“ tube and scale, weirs, 298. 

“ Woltman’s, 322. 

Gauges and weights of plate iron, 487, 488. 
Gauging, hydrometer, 316, 321. 

of mountain streams, 296. 

“ “ rainfall, 62. 

“ “ rivers, 318, 319. 

Gears for sluice-gates, 359. 

General rainfall, 46. 

Geological science, application, 106. 
Granular stability of masonry, 402. 
Graphical representation of force, 175, 402. 
Gravitation system, 588, 590. 

Gravity, 185, 187, 189, 190, 230, 299. 

“ centre of, 177, 391, 402. 

Great rain-storms, 61. 

Grouped rainfall statistics, 52. 

Grouting, 353, 369. 


H. 

Hardening impurities, 125. 

Hardness of water. 125. 

Head, desirable for fire-service, 493. 
“ effective in pipe-system, 493. 
“ how to economize, 276. 

“ loss by friction, 493. 

“ subdivisions of, 225. 

“ value of, 493. 

Heat, units of, utilized, 578. 
Heights, falling bodies, 187, 190. 

Yt of waves, 388. 


Hirsch’s sugar test of water, 150. 

Helpful influence of water supplies, 27. 

Hook gauge, Boyden’s, 296. 

“ “ use to detect fluctuations, 3x9. 

Horse-power of effluent jet, 225. 

“ “ to produce flow, 561. 

Hose streams, 510, 520. 

“ use of water, 34. 

Hudson river basin, 101. 

“ valley rainfall in, 53. 

Hydrants, 516. 517, 519, 522. 

“ high pressures, 522. 

“ streams, 520, 585. 

Hydraulic, excavation, 376. 

“ masonry, 369. 

“ mean depth, 235. 303, 441. 

“ “ radius, 236, 445. 

“ power pumping, 589, 591. 

“ proof of pipes, 477. 

Hydrometers, Castellis’ and others, 326. 

“ coefficients, 325, 326, 326^. 

“ gauging with, 316, 325, 326. 


I. 

Ice covering of canals, 372. 386. 

“ impure, in drinking water, 135. 

“ thrust, 358, 386. 

Impounders, flow to, 86. * 

Impounding of water, 144. 

Impregnation of water, 141, 152. 

Impurities of water, 112. 

“ “ “ agricultural, 134. 

“ “ atmospheric, 122. 

“ “ manufacturing, 134. 

“ “ “ mineral, 115, 133, 

“ " organic, 116, 127, 130. 

sewage, 134. 

“ “ “ sub-surface, 123. 

“ “ deep wells, 125. 

Inch and foot, decimal parts of, 457. 

Incidental advantages of water supplies, 29. 
Inclination in channels, 235, 304, 371, 372, 373. 
Increase in use of water, 39. 

Indian embankments, 334, 

Indicator, stop-valve, 361. 

Infiltration, 537, 540, 543, 544, 546. 

Influent chamber, 366. 

Infusoria, 130. 

Inhabitant, supply per, 40. 

Inspections of stand-pipe materials, 590, 601. 
Intercepting well, 102, 546. 

Interchangeable pipe-joints, 469. 

Introduction of filters, 551. 

Insurance schedule, 29. 

Investment, value of water supplies as an, 29. 
Iron, gauges and weights, 488. 

“ sluice valves, 360. 

“ work, varnishes for, 474, 476, 489. 
Irrigation canals. 370, 372, 373. 

Isolated weirs, 383. 


J. 

Jets, 211, 267. 

“ coefficients of velocity and contraction, 
196, 198, 208. 

“ contraction, 208. 

“ varying forms of, 211. 

“ velocity, 208. 

Joints, mortar for pipes. 487. 

“ of cast pipes, 457, 461, 463, 469. 


K. 

Kutter’s coefficients for channels, 305. 





INDEX. 


639 


L. 

Lake waters, 142. 

Lakes, 150. 

Laying of wrought-pipes, 482. 

Lead, joint, 468. 

Lead-pipes, 629, 630, 631. 

Lengths of waste-weirs, 381. 

Level, use of, in gauging, 319. 

Leverage of water-pressure, 397. 

“ resistance of walls, 402. 

“ stability of masonry, 39?. 

Life of dams, 388. 

Limiting pressure in masonry, 686. 

Lining of pipes, cement, 481. 

Logarithms of ratios, 121. 

Loss by evaporation, 87. 

“ from reservoirs. 84. 

“ of head by friction, 276, 493. 

M. 

Mains and distribution pipes, 446. 

“ power to produce flow in, 561. 
Masonry, angles of repose, 396. 

“ coefficients of friction, 396. 

“ concrete, 429, 430. 

conduits, 431, 437. 

“ coverings of waste pipes, 357. 

“ examples of pressure in, 392, 397, 
403, 406, 412. 

“ faced embankment, 354, 409,418, 423, 

425- 

*• frictional stability of, 402. 

“ granular stability of, 402. 

“ hydraulic, 369. 

“ limiting pressures in, 403, 404, 586. 

“ step and curve batters, 383, 385, 387, 
424. 

“ weight leverage of, 398. 

“ “ of, 395, 397, 404, 420. 

Materials, embankment, 339, 341, 342, 345, 348, 
35 I i 354 - 

“ of stand-pipes, 590. 

Maximum velocities of flow, 508. _ 

Mechanical energy of effluent water, 225. 
Metal plates, tests of, 590, 591. 

Metals for stand-pipes thickness, 595, 596, 597, 
598, 601. 

“ pipe, 470, 472. 

“ tenacities of wrought, 451,454, 486, 491. 
Meters, current, 322, 325, 326, 326a. 

Metric weights and measures, 611. 
Microscopical examination of metals, 471. 
Mineral impurities, 115, 530. 

“ springs, 142, 143. 

Miners’ canals, 375. 

Misapplication of formulae, 316. 

Mississippi valley, rainfall in, 54. 

Molecular theories, 162, 296. 

Molecules, 185. 

Moment of earth leverage, 412. 

Monads, 130. 

Monthly and hourly variations in the draught, 
41. 

“ fluctuations in rainfall, 56. 

Mortar for lining and covering pipes, 487. 
Motion, acceleration of, 185. 

“ equations of, 186. 

“ of a piston, 562. 

“ of water, 184, 194. 

“ parabolic, of a jet, 187. 

Moulding of pipes, 451. 

Moulinets, 323, 326. 

Municipal control of water supplies, 28. 

N. 

Natural clarification, 149, 532. 

“ laws, uniform effects of, 61. 


Necessity of water supplies, 25. 
Noctos, 129. 


O. 

Ohio river valley, rainfall in, 54. 

Open canals, 370. 

Ordinary flow of streams, 80. 

Organic impurities, 80, 113, 116, 531, 532. 
Organisms, 129, 131, 133. 

Orifice, submerged, 209. 

“ volume of efflux, 211. 

Orifices, classes of, 194. 

“ coefficients for circular, 196, 198, 199, 
203. 

“ coefficients for rectangular, 198, 200, 
201, 202, 205, 206. 

“ convergent, 212. 

“ path toward, 194. 

“ cylindrical and divergent, 2x2. 

experiments with, 198, 199, 200, 201. 

“ flow of water through, 194, 210. 
Orifice-jet, form of submerged, 195. 

“ peculiarities, 207. 

ratios of minimum section, 195. 

“ variations, 204. 

“ velocity, 196, 208, 209. 


P. 

Pacific coast rainfall. 54. 

Painting iron work, 476. 478, 489. 

Parabolic path of jet, 187. 

segment, application to weir vol¬ 
umes. 282. 

Partitions and retaining walls, 390. 

Paving, concrete, 355. 

“ embankment slope, 348, 350, 354, 355, 
356 , 358. 

Peculiar water sheds, 71. 

Penstock, cylindrical wood ? 439, 441. 
Percentages of rainfall on river basin, 73, 833. 
Percolation from reservoirs, 85, 94. 

“ of rain, 104, 105, in. 

“ under retaining walls, 406. 

Permanence of water supply essential, 585. 
Persons per family, 32, 33^. 

Physiological effects of the impurities of water, 
114. 

‘‘ office of water, 25. 

Pipe, adjustable effluent, 364. 

“ and conduit, 223. 

“ branches, composite, 484. 

“ coverings, 481, 487, 489, 501, 502. 

“ distribution, 493, 495, 503, 505, 506, 508. 

“ joints, cast, 457, 461, 463, 469, 483. 

“ “ “ hub, on wrought, 483. 

“ “ dimensions of, 451, 459, 462. 

“ “ flexible, 463, 464. 

“ “ interchangeable, 469. 

* k metals, 470, 472. 

“ wrought strength of, 451, 454, 
468, 490, 491. 

“ resistance at entrance to, 226. 

“ shells, wrought, thickness of, 448, 485, 
486. 

“ systems, duplication in, 510. 

“ “ illustrations, 493,510. 

“ testing press, 477. 

walls, resistances of. 227, 228. 

Pipes and sluices, embankment, 355. 

“ casting of, 452. 

“ cast-iron, 447, 451, 452. 

“ “ thickness of, 453, 454, 455, 466. 

“ “ weights of, 465, 468, 469. 

“ cement-joints, 482. 

“ “ lined. 479, 481. 

“ coefficients cf friction, 236, 242, 248, 495. 





640 


INDEX 


Pipes, concrete foundations for, 487. 

‘ contents of, 504. 

“ direct pressure systems, 525. 

“ depths of, 501, 502. 

“ “ sockets, 459, 461. 

“ diameters for fire supplies, 510. 

“ elementary dimensions of, 504. 

“ expansions of, 458. 

44 flanges, table of, 462. 

“ formulas for thickness of cast, 453, 466. 

“ “ *• velocity, head, volume and 

diameter, 224, 266, 268, 270, 498. 

“ formulas for weights of cast, 465. 

“ friction in, 222, 495, 508. 

“ hydraulic, proof of, 477. 

“ lead in joints, 468. 

“ mains and distribution, 446. 

44 molding of cast-iron, 451. 

“ plan of a system, 505. 

“ preservation of surfaces, 473, 480, 489, 
491. 

44 proof tests, 476. 

“ relative capacities of, 498, 500. 

“ service, 527, 528. 

“ short, 223. 

“ square roots of fifth powers of diam¬ 
eters, 499, 500. 

“ static pressure in, 446. 

“ sub-coefficients of flow (c'), 271. 

“ temperatures of water in, 502. 

“ thickness of cast, 453, 455, 456. 

“ “ wrought, 447, 450, 486, 488. 

“ tuberculated, 247, 248. 

“ volumes of flow from, 223, 225, 495. 

“ water-ram in, 448, 449. 

“ wood, 491. 

“ wrouglit-iron, 479. 

“ “ plates for, 490. 

Piping and water sunplied, 38. 

“ ratio to population, 35. 

Piston motion, 562. 

“ pump, 557, 558. 

Pitot tube gauge, 320. 

Plant and insect agencies, 147. 

“ growth in reservoirs, 145. 

Plates for wrought pipes, 490. 

Plunger pump, 557, 563. 

Pluviometer, 63. 

Polluted water, definition of, 137. 

Polluting liquids, inadmissible, 154. 

Pollution question, 156. 

“ of water, artificial, T52. 

Population, and relation of supply per capita, 
40. 

*• of various cities, 32, 33a, 33^. 

Portland cement for joint mortar, 487. 

Porosity of earths and rocks, 102. 

Post hydrants, 517. 

Power consumed by variable flow in a main, 
560. 

“ consumed in pumps, 560, 561. 

“ required to open a valve, 361, 364. 

Practical construction of water-works, 333. 

Precautions for triangular weirs. 295. 

Precipitation, influence of elevation upon, 50. 

Preservation of pipe surfaces, 473, 480, 489, 

„ 491 * 

Press for testing pipes, 477. 

Pressure, a line a measure of, 174. 

“ conduits under, 435, 439, 440. 

“ conversion into mechanical effect, 

230. 

“ conversion of velocity into. 227. 

“ direction of maximum effect, T76. 

“ in stand-pioes, 593. 

“ leverage of water, 397. 

44 of earth against walls, 408, 410, 413, 
415, 416. 

“ of water, 168, 172, 446. 


44 

44 

44 

44 


44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 


Pressure of water in a conduit. 437. 

“ proportional to depth, 169, 172. 
resultants, 391, 400, 411, 418, ^23. 
sustaining upon floating bodies, 179. 
transmission of, 183. 
upon a unit of surface, 171. 

“ upon surfaces, 391, 393. 

“ weight a measure of, 173. 

Pressures, artificial, 171. 

“ at given depths, table, 172. 
atmospheric, 182. 
centres of, 177. 
convertible into motion, 184. 
examples in walls, 403, 404. 
from inclined columns of water, 
170. 

f reat, in hydrants, 522. 

orizontal and vertical effects, 177. 
in embankments, 343. 
limiting in masonry, 403, 404. 
static in pipes, 446, 448. 
total of water, 176. 
upon circular areas, 179, 446. 

“ 44 curved surfaces, 178, 446. 

“ upward upon submerged lintels, 
181. 

Prism of weir volumes, 282. 

Processes for preserving iron, 474, 476, 489. 
Profile across the United States, 48. 

44 of retaining walls, 407. 

Properties of water, 113. 

“ “ embankment materials, 343. 

Proportions of 44 “ 349. 

Protection of filter beds, 548, 555. 

44 44 water supply channels, 431. 

Protective value of stand-pipes, 586. 

Prony’s analysis of experiments, 255. 

Proving press, hydraulic, 477. 

Puddled canal bank, 370. 

Puddle-wall, 351, 354. 

“ slope, 352, 356, 370. 

Pump, bucket-plunger, 557, 567, 603, 

“ Cornish. 557. 563. 

“ piston, 557, 558, 
plunger, 557, 563. 
rotary, 558, 

valves, 558, 563, 566, 568, 569, 570, 571. 
Pumping ot water, 557. 

“ diagram of, 42. 
engines, 557, 567, 573, 577. 

“ adaptability of, 584. 

“ cost of supplies, 575, 582. 

44 attendance, 575, 582. 
duties, 574, 579, 580, 581, 583. 
“ fuel expenses. 581, 582. 

“ principal divisions, 577. 

special trial duties, 580. 

44 values compared, 583. 
machinery', 591, 592. 603. 

contingencies, 586. 
duplicate, 608. 
for direct pressure, 590, 
S 9 1 - 

44 Manchester, 603, 609. 
system, 607, 608. 
water, cost of, 574, 575. 

Pumps, power consumed in, 560, 561. 

44 types of, 557. 

44 variable flow through, 559. 

Purity' of water, chief requisites for, 144. 

44 preservation of, 148. 
Purification of water, natural, 134, 157, 158. 


44 

U 


(4 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 

44 


4 4 
44 
44 


Q. 

Quality of water, sugar test of, 159. 


R. 

Radii, mean of conduits, 441, 442. 





INDEX. 


641 


Rainfall along river courses, 51. 

and equivalent flow, 82. 
diagrams of, 55, 57, 59. 
gauging, 62. 

“ general, 46. 

in the United States, 53. 

“ influences affecting, 60. 

“ low cycle, 69, 77, 78. 

monthly fluctuations in, 56. 
on Cochituate Basin, 72, 73. 

“ Croton Basin, 83a. 

“ ratio of floods to, 62. 

ratios, 72, 100, 101. 
secular fluctuations in, 60. 

“ sections of maximum, 47. 

statistics, review of, 46, 72, 83a. 

“ volumes of given, 62, 83a. 

Rainfalls, flow from given, per acre and per 
mile, 82. 

Rain-gauge, 63. 

Rains, river basin, 50, 72. 

Rain, water in pipes, 449. 

Rates of fire supplies. 506. 

Rating of current meters, 325, 326, 328a. 

Ratios of evaporation, 91. 

“ monthly consumption, 43. 

“ “ flow in streams, 76, 101. 

“ “ qualification of deduced, 99. 

“ “ rainfall, flow, etc., table, 72, 100,101. 

“ “ standard gallons, 120. 

“ surface to mean velocities in chan¬ 


nels, 315. 

“ “ variable delivery of water, 564. 

“ “ water storage, 95, 97. 

Reaction and gravity, opposition of, 230. 
Reconnaissance for embankment site, 346. 

“ of a water-shed, 78. 

Rectangular and trapezoidal walls, moments 
of, 399. 

Rectangular weirs. 277. 

Reducer, pipe, 478. 

Register, electric current meter, 325(2. 

Relation of supply per capita to total popula¬ 
tion, 40. 

Relative values of h , h\ h" } 253. 

“ discharging capacities of pipes, 498, 


500. 

“ rates of domestic and fire draughts, 
508. 

Repulsion, molecular, 296. 

Reserve for fire service, 44. 

Reservoir, coverings, 556. 

“ distributing, 334, 353, 354, 356, 358. 
“ embankments, 333»335,34U 345, 348, 

353 * 

“ storage, surveys for, 347. 

“ strata conditions in, 146. 

“ system, 598. 

“ revetments, 354. 

Reservoirs, failure of, 334. 

“ Indian, 334. 

“ storage, 84, 87, 93, 95, 97, 101, 347. 

“ subterranean, 105. 

“ waves upon, 388. 

Resistance of the air to a jet, 190. 

“ at entrance to a pipe, 266. 

“ of masonry revetments, 417. 

“ to flow, measure of, 230, 231. 

Resistances to flow within a pipe, 227, 229, 230, 
233, 248. 254, 256, 266, 272, 493 - 
Resistances to flow in channels, 300, 304, 307, 


3 IQ , 3 12 - 

Resultant effect of rain and evaporation, 92. 
Retaining walls, 390, 395, 397, 399, 406, 417, 420, 
425, 426. 

“ “ effect of traffic, on, 425. 

“ “ for earth, table. 420. 

“ ‘ front batters, 424. 

“ “ percolation under, 406. 


Retaining walls, sections of, 354, 407. 

“ “ top breadths, 424. 

Resultants in stand-pipes, 597, 

“ of pressure, 391, 400, 411, 418, 423. 
Revetted conduits, 431. 

‘ k embankment, 149, 354, 370, 429. 
Revetments, faced and concrete, 429. 

“ final resultants, 418. 

“* resistance of, 417. 

trapezoidal, table of, 420. 
Riparian rights, 85, 86. 

Rip-rap, slope, 371. 

River basin rains, 50. 

“ basins of Maine, 84. 

“ courses, rainfall along, 51. 

“ pollution committee, 154. 

“ waters, 151. 

Rivers and canals, table of flows, 307. 

Rivets, joints, 591, 592. 

“ table of, 592. 

Riveting, 591, 592. 

Roof for filter beds and reservoirs, 548, 555. 
Rotary pump, 558. 

Rubble, grouted, 353. 

“ masonry, 252. 

“ priming walls, 352. 

S. 

Safetv, factors of, 449, 451, 453, 485, 486, 593, 
594, 595 , 598, 600. 

Sand in embankments, 353. 

Sanitary discussions, 152. 

“ improvements, 26. 

“ office of water, 26. 

“ views, precautionary, 154. 

Schussler’s process of coating pipes, 489. 
Screens, fish, 365. 

Seasons of floods, 68. 

Sections of maximum rainfall, 47. 

Secular fluctuations in rainfall, 60. 

Sediments, 530, 531. 

Service pipes, frictions in, table, 528. 

Services, high and low, 524. 

Settling basins, 550. 

Sewage impurities, 134. 

“ “ dilution of, 153, 155. 

Shells of conduits, 434. 

Sheet-iron, gauges and weights, 488. 

Sheet piles, 371. 

“ under embankment, 339. 
Short-tubes, 215, 216. 

Showers, source of, 45. 

Sines of slopes, table, 259. 

Siphon, 182, 184. 

Site for embankment, reconnoissance for, 346. 
Skillful workmanship required, 369. 

Sleeves, pipe, 479, 482. 

Slope, earthwork, 344, 345. 

u of channels, 302, 307, 308, 310, 329. 

“ paving, 348, 354, 355, 356, 358. 

“ puddled, 352. 

“ “ embankment, 356. 

Slopes, velocities for given, 258. 

Sluice areas, 360. 

“ apertures, coefficients for, 201, 202, 203, 
205, 206. 

“ gate areas, 359. 

“ temporary stop-gate, 359. 

“ tunneled, embankment, 356, 358. 

“ valves, iron, 360. 364. 

Sluices, flow through, 200, 201, 203, 205, 206. 

“ high and low, 204. 

“ varying head on, 204. 

Smith’s (A. F.) adjustable pipe, 364. 

Soils beneath embankments, 337. 

“ evaporation from, no. 

Solutions, organic, 532. 

“ in water, 112. 






642 


INDEX. 


U 

44 

44 


44 

44 

44 

44 


44 

44 


44 

44 


Springs and wells, 102. 

“ “ “ supplying capacity of, no. 

mineral, 141. 

under embankments. 337. 

“ waters, 141. 

Stable use of water, 34. 

Stand-pipe foundations, 586. 

“ materials, 590, 594, 595, 596, 597, 601. 
Stand-pipes, 526, 564, 585, 602, 628. 

exposed, ix., 585, 598, 599, 628. 

“ moments of resistance, 588, 589. 
overturning tendency, 588. 
pressures in, 593. 

“ . on, 599. 
stabilities, 589, 597. 

Tank, ix., 585, 628. 

“ wind strains on, 587. 

Static pressures in pipes, 446. 

Stones, building, strengths of, 404. 

Stop-gates in conduits, 374, 436. 

Stop-valve, Coffin’s, 493. 

curbs, 515. 

Eddy’s, 511. 

Flower’s, 493. 

Ludlow’s, 514. 
system, 511. 

Stop-valves, 360, 374, 436, 493, 511, 513, 514 . 
Storage, additional, required, 98. 

“ basins, percolation from, 85. 

“ “ substratas of, 85. 

losses of water, 84. 
of water, 84. 

“ “ effect of evaporation on, 93. 

“ “ influence upon continuous 

supply, 99. 

“ “ required, 95. 

reservoir, 84, 87, 03, 95, 97, 101, 338. 

“ embankment, 553. 

“ substrata, 85. 

“ supply to, and draught from, 

table, 96. 

Storms, great rain, 61. 

Strata, conditions, 146. 

Strains on stand-pipes, 590, 593, 599. 

Streams, annual flow of, 77. 

“ available annual flow, 94. 

“ estimates of flow, 65, 78. 

“ flashy and steady, 71. 

“ gauging, 296, 316, 320, 322, 326. 

“ mean monthly flow of, 79. 

“ minimum, mean, and flood flow, 75. 

“ ordinary flow of, 80. 

“ ratio of monthly flow, 76. 

Strength of cylindrical cantilevers, 599, 600. 

“ “ hollow cylindrical beams, 600. 

Strengths of building stones, 404. 

‘‘ “ cylinders, 448, 593. 

“ “ metals, 451, 454. 

“ “ riveted joints, 591. 

“ “ wrought pipe metals, 451, 486, 491, 

Sub-heads compared, 253. 

Sub-mains, diameters of, 507. 

Submerged orifices, 209. 

Subterranean reservoirs, 105. 

“ waters, 102. 

“ watershed. 109. 

“ waters, temperatures of, 126. 

“ “ uncertainties of search 

for, 106. 

Substrata of a storage basin. 85. 

Sudbury river rainfall and flow, 83#. 

Supply main, diameter of, 506. 

“ to and draught from a reservoir, table, 
96, 97. 

Supplying capacity of watersheds, 94. 
Surcharged pressure, earth, 414, 416, 423. 
Surfaces, pressure of water upon, 391, 393. 
Surveys for storage reservoir, 347. 

Sources of water supplies, 587. 


it 

tt 


it 

ti 

it 

it 


Symbols, definitions of, 235. 

Systems, combined reservoir and direct, 525. 
“ of water supply, 603, 604. 

“ “ “ distribution, 493, 505. 

“ “ rainfall, 47, 49, 50, 


T. 


(See List of Tables, page xix.) 

Tank materials. 590. 

“ stand-pipes, ix., 585. 

“ “ lack of stability of, 587, 588, 

598, 600. 

Temperatures, artesian well, 127. 

of fleep sub-surface waters, 126. 

filter beds, 555. 

“ water in pipes, 502. 
Templets, for flange bolt-holes, 460. 

Tenacities of wrought-pipe metals, 431, 486, 


tt 

it 


49 1 * 

Tests of metal plates, 590, 591. 

“ “ pipe metals, 472, 590, 591. 

Testing of nydrometers, 325, 326. 

Theory of flow over a weir, 278, 280. 
Thicknesses of a curved-face wall, 422. 

“ “ dams, table, 387. 

“ “ pipes, formulas, 448, 450, 466, 

485, 486, 487. 

“ “ stand-pipe sheets, 595, 596, 597, 

601. 


“ “ walls for water-pressure, 399. 

“ “ wrought-pipe shells, 447, 486, 

488, 495, 597, 601. 

Thompson s molecular estimate, 162. 

Thrusts of a conduit arch, 437. 

Timber weirs, 384. 

Transit, use in gauging, 313, 318, 319. 
Transmission of pressures, 183. 

Traffic, effect upon retaining walls, 425. 
Trapezoidal revetments, table, 420. 
Treacherous strata beneath embankments, 338. 
Trial shafts, at embankment sites, 336. 
Trigonometrical equivalents, 618. 

Tube gauge, 317. 321. 

Tubes, coefficients of flow, 217, 219, 220. 

“ compound. 220. 

“ experiments with short, 217, 219, 220. 

“ short, 213, 215, 218, 220. 

Tubercles, in pipes, 247, 248. 

Turbine water-wheels, 559, 585, 593, 597. 
Turned pipe-joints, 458. 

Type curves of rainfall, 55, 57, 59. 


U. 

Uniform effect of natural laws, 61. 
Union of high and low services, 524. 
Units of heat utilized. 578. 

Use of water increasing, 39. 


V. 

Vacuum, ajutage, 214. 

“ imperfect, short tubes, 215. 

“ rise of water into, 182. 

“ tendency to in compound tubes, 221. 
“ under a weir crest, 292. 

Values of c\ 271. 

“ “ h and h\ table, 264. 

“ pumping engines compared, 583. 

“ “ water supplies as investments, 29. 

Valves, air, 523. 

“ blow-off, 5x3. 

“ Cornish, 569, 570. 

“ check, 525. 

“ curbs, 515. 

“ disk, 571. 

“ double beat, 5C9, 570. 

“ flap, 568. 





INDEX. 


643 


Valves, iron sluice, 360, 364. 

“ pis on, 569. 

“ power required to open, 361, 364. 

pump, 558. 563, 566, 568, 569, 570, 571. 
stop, 364, 493, 511, 513, 514. 
indicator, 361. 

44 system, 511. 

“ “ waste, 513. 

Vanne conduit, 438. 

Vapory elements, the, 45. 

Variable flow through pumps, 559. 

Varnishes for iron, 474, 476, 489. 

Vegetal growth in filter beds, 555. 

Vegetable organic impurities, 128. 

Velocity, conversion into pressure, 227. 

equation, modification of, 270. 

“ formula for, 249, 250. 

formulas for pipes, 249, 250, 252, 254, 
259, 263, 266, 267, 268, 270, 273. 

Velocities in canals and channels, 302, 307, 308, 
310, 312, 314, 318, 220, 325, 326, 330. 371, 373. 

Velocities for given slopes, table, 259. 

of falling bodies, table, 190. 

44 flow in pipes, 236, 243, 249, 254. 

“ given films in channels, 311. 
ratios of surface to mean, 315. 
relative, due to different depths in 
channels, 328. 
surface in channels, 313. 

“ theoretical table, 190. 

Vermin in canal banks, 371. 

Vertical shifting of water, 365. 

Virginia City, wrought-iron pjpe, 489. 

Voids of earths and rocks, 103* 

Volume delivered by pipes, table, 495. 

“ of efflux from an orifice, 194, 209. 

“ “ “ formula for, 196. 

“ “ hydrant streams. 585. 

“ flood inversely as the area of the 
basin, 65. 

Volumes, formulas, for flood, 65 

“ flood, from watersheds, 381. 

“ relative, due to different depths in 
channels, 328. 

“ of given rainfalls, 62. 

“ for given depth upon weirs, 290. 

“ from waste weirs, table, 380. 


W. 

Walls, back batters of, 422. 

44 chamber, 369. 

“ counterforted, 427. 

“ curved face, table, 422. 

“ earth pressure against, 408, 410, 412,413, 
415, 416. 

“ elements of failure, 427. 

44 end supports of, 429. 

“ front batters of, 424. 

44 formula of thickness for water pressure, 
399 - 

“ foundations of, 395, 406, 407. 

“ leverage resistance of, 402. 

“ limiting pressures in, 404. 

44 of concrete, 429, 430. 

“ profiles of, 407. 

“ retaining, 390, 393, 397, 399, 406, 417, 420, 
425, 426. 

“ to retain water, table, 400. 

“ 44 sustain traffic, 425. 

“ top breadths, 424. 

“ wharf, 426. 

Waste pipes, embankment, 357. 

“ sluice, “ 356. 

“ valves, 513. 

“ weir aprons, 383. 

“ 14 ballast. 385. 

“ 44 caps, 387. 

“ “ formulas, 379. 


Waste weir volumes, table, 380. 

weirs, 377, 381. 386, 387. 

44 discharges over, 378. 

“ “ effect of ice on, 386. 

“ “ forms of, 382. 

“ lengths for given watersheds, 381. 
“ “ thickness, table, 387. 

Water, analyses of potable, 117. 

“ characteristics of, 113, 159, 161. 

“ choice of, 605. 

“ clarification of, 530. 

44 commercial use of, 34. 

“ compressibility and elasticity of, 167. 

“ consumption of, 34, 503. 

44 crystalline forms of, 165. 

44 domestic use, 34. 

44 engine, 569. 

44 evaporation from, 88, 89. 

44 expansion of, 164, 166. 

44 flow of, 184. 194. 

44 force of falling, 388. 

“ hose, use of, 34. 

44 impregnations, 112, 141. 

44 impurities, 112, 141. 

44 molecular actions, 168. 169. 

44 physiological office of, 25. 

44 44 effect of the impurities of, 


114. 

Water pipes, organisms in, 129, 133. 

44 plant and insect agencies in, 147. 

44 pressure leverage of, 397. 

44 44 upon surfaces, 168, 176, 391, 

393. 

44 pumping of, 557. 

44 rarity of clear, 530. 

44 ratios of variable flow, 564. 

44 relative volumes and temperatures, 166. 
44 river, 151. 

44 sanitary office of. 26. 

44 solvent powers of, 113. 

44 spring, 141. 

44 storage of, 84, 

44 subterranean, 102. 

44 sugar test cf quality, 159. 

44 supplied, 31, 35, 36, 37, 38, 40. 

44 supplies, gathering and delivery, 586. 

“ supplies, incidental advantages of, 29. 

44 44 necessities of, 25. 

44 supply, gravity, 606. 

44 44 permanence of, 603. 

44 44 systems of, 603. 

44 the composition of, 112. 

44 vertical changes in, 365. 

44 volumes and weights', table, 161, 164, 
166. 

44 waste, 34. 

44 weight of constituents, 164. 

44 44 pressure and motion of, 161. 

44 well, 139. 

44 wheels. 559, 579. 

“ works, construction of, 333. 

44 ram in pipes, 449. 

44 sheds, 71, 100. 

44 44 flood volumes, 62, 67, 68, 75, 98, 

380, 381. 

44 44 flow from, 96. 

44 44 supplying capacity of, 94. 

44 44 waste weirs required, 381. 

Weights and measures, metric, 611. 

Weir apron, 279. 

44 benches, 384. 

44 caps, breadths, 386, 387. 

44 coefficients, 288, 289, 291. 

44 crests, 278, 292, 293. 

44 gauging, 77. 

44 over falls, 377. 

Weirs, crest contractions, 280. 

44 dimensions of, 278, 279, 386, 387. 

44 discharges over, table, 289, 289a, 290. 




644 


INDEX. 


Weirs, experiments with large, 284. 

“ forms of, 277, 386, 387. 

“ formula tor wide-crested, 293. 

“ “ “ depth upon, 286,287. 

“ formulas, 282, 283, 284, 286, 

“ gratings in front ot, 292. 

“ book-gauge for, 297, 

“ initial velocity ot approach to, 285, 292. 
“ isolated waste, 383. 

*• measuring, 277, 295. 

“ rule gauge for, 298. 

“ stability of, 279, 386, 387. 

“ tail-water of, 292. 

“ thickness of waste, 386, 387. 

“ triangular notch, 294, 295. 

“ tube and scale-gauge for, 298. 

“ timber, 384. 

“ varying lengths, 279. 

u volumes, formulas for, 282, 283, 284, 
286, 287, 293. 

“ waste, 337, 383, 386, 387. 

“ wide-crested, 293. 

Weight, a line a measure of, 173. 

“ a measure of pressure, 173. 

“ and volume of water, table, 166 
“ leverage of masonry, 398. 

“ of pond-water, 167. 

Weights of cast pipes, 465, 468, 469. 


Weights of embankment materials, 341, 342, 
411. 

“ “ molecules, 168. 

Well, intercepting, 546. 

“ water, 139. 

“ waters, analyses of, 121. 

Wells and springs, 102, no. 

“ condition ot overflowing, 107. 

“ fouling of old, 140. 

“ influence upon each other, 107. 

impurities of deep, 125. 

“ location lor, 139. 

“ water-sheds of, ic8. 

Western rain system, 47. 

Wharf, cap-log, 426. 

“ fender and belay piles, 427. 

“ walls, 426. 

Wind leverage on tanks, 588, 589, 598, 599. 

“ strains on stand-pipes, 587. 

Winds, destructive actions. 586, 587. 

“ resultant on curved surface, 587. 

Wood pipes, 491. 

Woltmann’s tachometer, 322. 

Workmanship, skilliul, 369. 

Wrought-iron pipes, 479. 

“ “ pipe-joint, cast, 483. 

“ “ plates, gauges and 'weights, 488. 

Wyckoff’s wood-pipe, 491. 




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